Create a model that tells the sign of the product of a negative number times a positive
number.
Answers
Multiplying by a negative is repeated subtraction. When we multiply a negative number times a negative number, we are getting less negative. This analogy between multiplication and addition and subtraction helps students nicely connect the two concepts.
When you have two negative signs, one turns over, and they add together to make a positive. If you have a positive and a negative, there is one dash left over, and the answer is negative.
When We Multiply:
Example ⬇️
× two positives make a positive: 3 × 2 = 6
× two negatives make a positive: (−3) × (−2) = 6
× a negative and a positive make a negative: (−3) × 2 = −6
× a positive and a negative make a negative: 3 × (−2) = −6
I hope this helps!!
Related Questions
Graph the system of equations on your graph paper to answer the question.
{y=x−4y=−x+6
What is the solution for this system of equations?
Answers
Answer: (5 , 1)
Step-by-Step explanation:
hihi your problem is a system of question y = x-4 and y = -x+6 okay so graph them both normally and then find the point where they intersect which is gonna be a coordinate point, and that's your solution !!
y = x-4
the y intersect is going to be 4
the slope is a positive 1 , going up to the right, through the positive quadrant, line is facing to the right
y = -x+6
the y intersect is going to be -6
the slope is going to be a -1 , following up the opposite way the line is going to face the left
once you graph them both you'll see the point of intersection, the solution
make sure you drew your lines very clearly !!!!
the solution is x = 5 and y = 1 which is also (5 , 1)
hopefully this was helpful !
an Expression for difference of a number s and -6
Answers
After answering the given query, we can state that The expression for the difference between a number s and -6 is: s - (-6) or s + 6
what is expression ?In numbers, you can multiply, split, add, or take away. The following is how a phrase is made together: Numeric number, expression, and arithmetic operator The elements of a mathematical expression are integers, factors, and functions. It is feasible to use contrasting words and terms. Any mathematical declaration containing variables, integers, and a mathematical action between them is known as an expression, also known as an algebraic expression. As an example, the expression 4m + 5 is composed of the expressions 4m and 5, as well as the variable m from the provided equation, which are all separated by the mathematical symbol +.
The expression for the difference between a number s and -6 is:
s - (-6)
or
s + 6
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3. (05.06 MC)
Graph the system of Inequalities presented here on your own paper, then use your graph to answer the following questions:
y < 4x – 2
y>5/2x-2 (should be the greater than or equal to sign)
Part A: Describe the graph of the system, including shading and the types of lines graphed. Provide a description of the solution area. (6 points)
Part B: Is the point (-2,-2) Included in the solution area for the system? Justify your answer mathematically. (4 points)
(10 points)
Answers
9514 1404 393
Answer:
A) The first inequality has a dashed boundary line with a slope of 4 and a y-intercept of -2. The shading is below the line. The second inequality has a solid boundary line with a slope of 5/2 and a y-intercept of -2. The shading is above the line. The solution space is a narrow wedge extending up and to the right of the y-intercepts at (0, -2) through the fourth quadrant into the first quadrant.
B) Not in the solution space. The point does not satisfy y < 4(-2) -2 because -2 is not less than -10.
Step-by-step explanation:
Part A:
The boundary line of each inequality is in slope-intercept form, so can be drawn easily by finding points with the appropriate slope=rise/run from the common y-intercept at (0, -2).
The first inequality does not include the "or equal to" case, so the boundary line will be dashed. The relation of y and the inequality symbol is y < ( ), so the shading will be below the line, where y-values are less than those on the line.
The second inequality includes the "or equal to" case, so the boundary line is solid. The relation of y and the inequality symbol is y ≥ ( ), so the shading will be above the line, where y-values are greater than those on the line.
The two shaded areas overlap in a narrow wedge between lines with slope 2.5 and 4. The lower-left point of the wedge is the common y-intercept at (0, -2). It extends through the fourth quadrant into the first quadrant. This wedge is the solution area.
__
Part B:
Based on the above description, no part of the solution space is in the third quadrant, where the point (-2, -2) lies. The point is not in the solution space. It does not satisfy the first inequality:
\(-2\nless(4)(-2)-2=-10\)
Instructions
In this experiment, you will be using two different coins as a simulation for a real-world compound event.
Suppose that a family has an equally likely chance of having a cat or a dog. If they have two pets, they could have 1 dog and 1 cat, they could have 2 dogs, or they could have 2 cats.
1. What is the theoretical probability that the family has two dogs or two cats?
let dogs be heads. Let cats be tails. A coin has two sides, in which you are flipping two of them. two cats and two dogs is 50%
2. Describe how to use two different coins to simulate which two pets the family has.
By saying that if a higher number of times the coin had landed on a certain side, then that
would mean what pair of animals you would get.
3. Flip both coins 50 times and record your data in a table like the one below.
Result Frequency
Heads, Heads 10
Heads, Tails 22
Tails, Heads 16
Tails, Tails 12
Total 60 sorry typo
4.
5. Based on your data, what is the experimental probability that the family has two dogs or two cats?
Based on my data it would be 44 percent for two dogs and 32 percent for two cats.
6. If the family has three pets, what is the theoretical probability that they have three dogs or three cats?
6 out of 9.
7. How could you change the simulation to generate data for three pets?
I would use three coins and change the total to make it an even number of flips.
Answers
Answer:
Step-by-step explanation:
let dogs be heads. Let cats be tails. A coin has two sides, in which you are flipping two of them. Note that there can be the possible outcomes
h-h, h-t, t-h, t-t.
How this affects the possibility of two dogs & two cats. Note that there are 1/2 a chance of getting those two (with the others being one of each), which means that out of 4 chances, 2 are allowed.
2/4 = 1/2
50% is your answer
Heads represents cats and tails represents dogs. There is two coins because we are checking the probability of two pets. You have to do the experiment to get your set of data, once you get your set of data, you will be able to divide it into the probability for cats or dogs. To change the simulation to generate data for 3 pets, simply add a new coin and category for the new pet.
A swimming pool drains 365.6 gallons of water over a period of 8 hours. What is the rate of change in the swimming pool?
Answers
Answer:
rate of change = 365.6/8
45.7
.......... Hope it helps
Answer:
45.7 gal/hr
Step-by-step explanation:
Divide the volume of water by the time interval to find the unit rate of change:
365.6 gal
------------------ = 45.7 gal/hr
8 hrs
Jarred went to the bookstore,
He bought a softcover book which was on sale for 10%
off. He spent $18 on the book, What was the original
price?
Answers
Answer:
the original price of the book is $20
Step-by-step explanation:
sometimes in a question, they put things in the question that don't actually help us get to the answer. usually we ignore it, but i'm going to list them out just to help you a bit more.
Things that are useless:
his name is Jarred (his name could be gary, it doesn't affect us getting the answer)he went to a bookstore (he could've gone to the library, it wont affect us getting to the answer)the book is softcover (it could be any type of book, wont affect us getting to the answer)the item is a book (it could be anything that he bought, wont affect us getting to the answer.)Things that are helpful:
the book was on sale (helps us know that the price was reduced)the book was on sale 10% (helps us know how much it was reduced by)he spent $18 for the reduced price (helps us know how much he spent)Ok, now that we know those, let's work on the question.
let b be the original book price
we need to find 10% so we have to use 90% (because 100 - 10 = 90)
if we needed to find 20% we would use 80% (because 100 - 20 = 80)
and so on.
90% of b = 18 (90% of the og. book price equals 18)
90/100 × b = 18 (write a correct equation and make the percent a fraction)
9/10 × b = 18 (simplify both sides of the equation)
9 × b = 180 (multiply both sides of the equation to get rid of fraction)
b = 20 (divide both sides of the equ. to get b by itself)
the original price of the book is $20
hope this helped :D
good luck my friend
- cheesetoasty
The coordinates of Triangle ABC are A= (-1.1). B (3,-5) and C (3, 3). What is the area of the triangle?
Answers
Answer:
16 square units-----------------------------
We are given the vertices:
A= (-1.1). B (3,-5) and C (3, 3)Use the formula:
A = (1/2) * |(x₁ * (y₂ - y₃) + x₂ * (y₃ - y₁) + x₃ * (y₁ - y₂))|Plug in the coordinates of the vertices:
A = (1/2) * |((-1) * (-5 - 3) + 3 * (3 - 1) + 3 * (1 - (-5)))| = (1/2) * |(-1 * (-8) + 3 * (2) + 3 * (6))| = (1/2) * |(8 + 6 + 18)| = (1/2) * (32) = 16So, the area of triangle is 16 square units.
.54 oz of premium walnuts costs $12.95. what is cost per ounce
Answers
The cost per ounce of the premium walnut is $0. 23
What is proportion?To determine the value of the cost, we need to note that proportion is simply described as the comparison of numbers such that they are made equal to another.
From the information given, we have that;
54 ounces of premium walnuts costs $12.95
This is represented as;
54 ounces = $12. 95
Then 1 = x
cross multiply the values, we get;
x = $12.95/54
Divide the values, we get;
x = $0. 23
Hence, the value is $0. 23 per premium walnut
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Given the quadratic function
Answers
The vertex is (-4,-3)
The axis of symmetry is x=-4
and the transformations are:
A group of students want to build three identical rectangular gardens, each of
which has a width of x ft. The gardens will be arranged in one of two ways, as
showr by the plans below. The students have 480 ft of fencing and plan to build
a fenc around each of the three gardens. They will also install lighting for the
garders.
Plan A
Plan B
X
x
X
X
X
1. Suppose that the students use all of the fencing. Given that the width of a
small rectangular garden is x ft, write an expression in terms of x for the length
of one of the small rectangular gardens in Plan A. Then write an expression
in terms of x for the length of one of the small rectangular gardens in Plan B.
Explain.
Answers
So, here we have the following figures for each plan:
We're given that the students have 480 ft of fencing, and they want to build a fence around each of the three gardens.
If "x" represents the width, we could say that "y" represents the large.
To find an expression for the length of one of the small rectangular gardens in plan A, remember that the perimeter of a rectangle is defined as the sum of the measures of all its sides. So, the total fence in the plan A is given by the expression:
\(4x+6y=480\)We could solve this equation in terms of x to find the value of y:
\(\begin{gathered} 6y=480-4x \\ y=\frac{480-4x}{6}\to y=80-\frac{2}{3}x \end{gathered}\)Now, we're asked to find an expression for the length of one of the small rectangular gardens in plan A.
So, the perimeter of one rectangle will be the substraction between 480 and the perimeter of the other two small rectangles:
\(\begin{gathered} 480-(x+x+y+y+y+y) \\ 480-2x-4y \end{gathered}\)But we know that y = 80 - 2/3x, so:
\(\begin{gathered} L=480-2x-4(80-\frac{2}{3}x) \\ L(x)=480-2x-320+\frac{2}{3}x \\ L(x)=160-\frac{4}{3}x \end{gathered}\)So that's the expression for the length of one of the small rectangular gardens in plan A.
Now, for plan B, we got that the total length of the three gardens is,
\(5x+5y=480\)If we solve for y:
\(\begin{gathered} 5y=480-5x \\ y=96-x \end{gathered}\)And, the perimeter of one rectangle will be the substraction between 480 and the perimeter of the other two small rectangles:
\(\begin{gathered} L=480-(3x+3y) \\ L=480-3x-3y \end{gathered}\)But, we know that y=96-x, so:
\(\begin{gathered} L(x)=480-3x-3(96-x) \\ L(x)=480-3x-288+3x \\ L(x)=192 \end{gathered}\)That means that the value of the length in the plan B is constant.
How do you find the equation of the midline for a function?
Answers
Therefore , the solution to the given problem is the equation of the midline is: y = M+m /2 .
What is equation?An equation is a mathematical formula that connects two assertions using the equal sign (=) to denote equivalence. In algebra, an equation is a mathematical statement that establishes the equality of two mathematical expressions. For instance, an equal sign separates the components 3x + 5 and 14 in the equation 3x + 5 = 14. A mathematical formula is used to express the connection between two phrases on either side of a letter. Frequently, there is just one variable, which is also the symbol. for example, 2x - 4 = 2.
Here,
The midline equation is y = M+m /2
when a function has: o a max M AND a min m or o (if it does not have extrema) a bound above M and a bound below m, where M is the minimum bound above and m is the maximum bound below.
When one of the following conditions is true for a function, even though it has a bound below, there is no midline (even if it has a bound above)
It is solely constrained from above (or below)
Any line is midline if a function has the values (-∞, +∞)
Therefore , the solution to the given problem is the equation of the midline is: y = M+m /2 .
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A 15 meter long cylinder with a diameter of 7 meters has a square prism with a base length of 3 meters hole going all the way through the center of it as shown in the diagram (not to scale).
Find the volume of the composite shape rounding to the nearest cubic meter.
Hint: while working the problem carry figures at least three decimal places, then round to the nearest cubic meter only once at the very end.
Answers
The square prism's volume is 135 meter
Explain about the volume of the composite shape?Either the total number of smaller prisms that make up the composite shape, or its volume. the distinction between a larger prism and a smaller prism that was taken out of it.
A composite shape is a shape that was produced from two or more fundamental shapes. Composite shapes are also referred to as compound and complex shapes frequently.
Any shape that is constructed from two or more geometric shapes is referred to as a composite or compound shape. The triangle and square in the following shape are joined together. The square and the rectangle that make up the blue shape. There are two triangles making up the green shape.
Detailed explanation:
The parameters listed are;
L = 15 meters is the cylinder's length.
D = 7 meters is the cylinder's diameter.
B = 3 meters is the square prism's base length.
Consequently, we have;
The square prism's volume is
= B² x L
= 3² x 15
= 9 x 15
= 135 meter
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If leah has 22 boxes she gives 12 boxes to her mom how many boxes does leah have left
Answers
Subtract the amount she gives her mom from the total amount she has:
22 - 12 = 10
She has 10 boxes left.
Estimate 1.19 and 12
Answers
Answer:
The unit rate is about 10 cents per fluid once of grape of juice.
Step-by-step explanation:
John is constructing a satellite dish The receiver is going to be located 6 inches above the vertex of the dish. The dish is going to be 96 inches wide. How deep will the dish be?
- 84 inches
-92 inches
-96 inches
-88 inches
-none of the above
Answers
C. The depth of the dish is 96 inches.
Coordinate points of the parabola
The symmetry of the parabola indicates that when the depth is 6 inches, that the edge is 48 inches (half of 96) to the right and left of the axis of symmetry.
This implies that this parabola passes through (48, 6).
How high is the focus is above the vertex?To determine how high the focus is above the vertex. The conic form of a parabola with its vertex at the origin is given as;
y = (1/4c)x²
where;
c is the distance between the focus and the vertex.From the equation above, we can substitute the value of our coordinates and solve for c.
6 = (1/4c)(48²)
24c = 2304
c = 2304/24
c = 96 inches
Thus, the depth of the dish is 96 inches.
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Rewrite 2/5 : 1/15 as a unit rate
6.1
Answers
Answer:
Step-by-step explanation:
\(\frac{2}{5} : \frac{1}{15}\\\)
LCM of the denominator = LCM ( 5 , 15 ) = 15
∴ Now we have to multiply LCM by both the fractions , we get ,
\(\frac{2}{5}.15 : \frac{1}{15}.15\\ 6 : 1\)
At a dinner, the meal cost $22 and a sales tax of $2.09 was added to the bill. What is the tax rate for meals in this city?
Answers
Answer:
24.09 am I smart or what lol
Step-by-step explanation:
22 +2.09
17 divided into 3,536
Answers
Answer: 208
Step-by-step explanation:
The number 3536 is called the numerator or dividend, and the number 17 is called the denominator or divisor.
The quotient of 3536 and 17, the ratio of 3536 and 17, as well as the fraction of 3536 and 17 all mean (almost) the same:
3536 divided by 17, often written as 3536/17 = 208
How can the statement be rewritten as a conditional statement in if-then form?
A rectangle with 4 congruent sides is a square.
If a rectangle has 4 congruent sides, then it is a square.
If a figure has 4 congruent sides, then it is a square.
If a figure has 4 congruent sides, then it is a rectangle or square.
If a figure is a rectangle, then it is a square.
Answers
The statement be rewritten as a conditional statement in if-then form as If a rectangle has 4 congruent sides, then it is a square.
What is conditional statement ?A conditional statement is a statement that can be written in the form “If P then Q,” where P and Q are sentences. For this conditional statement, P is called the hypothesis and Q is called the conclusion. Intuitively, “If P then Q” means that Q must be true whenever P is true.
Given:
The conditional statement is A rectangle with 4 congruent sides is a square.
According to given question we have
The conditional statement is given as A rectangle with 4 congruent sides is a square.
The counterexample must satisfy the hypothesis of the conditional statement.
So, '' If a rectangle has 4 congruent sides, then it is a square.''
Therefore, the statement be rewritten as a conditional statement in if-then form as If a rectangle has 4 congruent sides, then it is a square.
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Answer: A
Step-by-step explanation:
i took it
A legend reads 1cm:15cm. If the scale drawing shows a ball that is 10cm in diameter, then what is the diameter of the ball in real life?
Answers
The diameter of the ball in real life given the scale of the drawing is 150cm.
What is the scale of the drawing?A scale drawing is a reduced form in terms of dimensions of an original image / building / object
Scale of the drawing = original dimensions / dimensions of the scale drawing
10cm x 15 cm - 150cm
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Find the equation(s) of the tangent(s) to the circle :2.1. \((x + 2 {)}^{2} + {y}^{2} = 4 \: at \: the \: x \: intercepts \: of \: the \: circle\)
Answers
The equation of a line with slope m that passes through the point (a,b) is:
\(y=m(x-a)+b\)On the other hand, if a curve is defined by a function y=f(x), the line tangent to the curve at a point (a,f(a)) will have a slope equal to f'(a), so the equation of the line tangent to the curve at (a,f(a)) is given by the expression:
\(y=f^{\prime}(a)(x-a)+f(a)\)Isolate y from the given equation to find an expression for f(x):
\(\begin{gathered} (x+2)^2+y^2=4 \\ \\ \Rightarrow y^2=4-(x+2)^2 \\ \\ \Rightarrow y=\pm\sqrt{4-(x+2)^2} \end{gathered}\)A function must have only 1 value for each input. In this case, y has two possible values for each given value of x. We want to explore the x-intercepts, which are given by the condition y=0. Then, any of the two signs is useful for this purpose. We will choose the positive sign. Then:
\(f(x)=\sqrt{4-(x+2)^2}\)Find the derivative of f:
\(\begin{gathered} f^{\prime}(x)=\frac{d}{dx}f(x) \\ =\frac{d}{dx}\sqrt{4-(x+2)^2} \\ =\frac{1}{2\sqrt{4-(x+2)^2}}\cdot\frac{d}{dx}\left(4-(x+2)^2\right) \\ =\frac{1}{2\sqrt{4-(x+2)^2}}\cdot-2(x+2) \\ =-\frac{x+2}{\sqrt{4-(x+2)^2}} \\ \\ \therefore\quad f^{\prime}(x)=-\frac{x+2}{\sqrt{4-(x+2)^2}} \end{gathered}\)Find the values of x that correspond to y=0:
\(\begin{gathered} \left(x+2\right)^2+y^2=4 \\ \Rightarrow\left(x+2\right)^2+0=4 \\ \Rightarrow\left(x+2\right)^2=4 \\ \Rightarrow x+2=\pm\sqrt{4} \\ \Rightarrow x+2=\pm2 \\ \Rightarrow x=-2\pm2 \\ \Rightarrow x_1=-4,x_2=0 \end{gathered}\)The x-intercepts are -4 and 0, but the denominator of the derivative is equal to 0 when x reaches any of those values, so the derivative diverges.
Then, the slope of the line tangent to the circle at the x-intercepts is not defined, which means that those lines are vertical lines.
Therefore, the equation of the lines tangent to the given circle at the x-intercepts, are:
\(\begin{gathered} x=-4 \\ x=0 \end{gathered}\)}^{2} + {y}^{2} = 4 \: at \:](https://i5t5.c14.e2-1.dev/h-images-qa/answers/attachments/AioxvKQWF3CPvDYiOeJzE2Kq83cuTNYY.png)
2(d+9)
I do not know this I need help
Answers
Answer:
Expanding the expression 2(d+9) gives:
2(d+9) = 2*d + 2*9
Simplifying the expression gives:
2(d+9) =2d + 18
Therefore, 2(d+9) is equivalent to 2d +18.
The simplified expression is:
↬ 2d + 18Work:
To simplify this expression, I distribute 2 through the parenthesis:
\(\sf{2(d+9)}\)
\(\sf{2\cdot d + 2 \cdot9}\)
\(\sf{2d+18}\)
Hence, the answer is 2d + 18.HELP please :)!!!!!!!!!!!!!!!!!!!!!!!!!!!!!asap
Answers
Answer:
B
Step-by-step explanation:
7100-3100
not sure though
Find the x-intercepts of the parabola with vertex (4,-1) and y-intercept (0,15). Write your answer in this form: (x1,y1),(x2,y2). If necessary, round to the nearest hundredth.
Answers
Answer:
(3,0) and (5,0)
Step-by-step explanation:
First let's write the generic model of a parabola:
\(y = ax^2 + bx + c\)
Now, using the points (0, 15) and (4, -1), we have:
(0, 15):
\(15 = 0a + 0b + c\)
\(c=15\)
(4, -1):
\(-1 =16a+4b+15\)
\(16a + 4b = -16\)
\(4a + b = -4\)
The x-coordinate of the vertex is given by the equation:
\(x_v = -b/2a\)
\(-b/2a = 4\)
\(b = -8a\)
Now, using this value of b in the equation \(4a + b = -4\), we have:
\(4a - 8a = -4\)
\(a = 1\)
\(b = -8\)
The x-intercepts are where we have y = 0, so:
\(0 = x^2 -8x + 15\)
Using Bhaskara's formula, we have:
\(\Delta = b^2 - 4ac = 64 -60 = 4\)
\(x = -b \±\sqrt{\Delta}/2a\)
\(x_1 = (8 + 2)/2 = 5\)
\(x_2 = (8 - 2)/2 = 3\)
So the x-intercepts are (3,0) and (5,0).
What comes next in this pattern 7, 11, 2, 18, -7?
Answers
Answer: 29
Step-by-step explanation:
64 players started how many left after 3 rounds
Answers
Answer: 8
Step-by-step explanation:
I do not understand the question. But if my interpretation is correct, then:
If there are 64 players and 3 rounds, 32 will get out in the first round. 16 will get out in the second, and 8 will get out on the third. Thus, the answer is 64-(32+16+8) or just simply 8.
Can I please get some help on this pretty please
Answers
Answer:
Score with 6 questions wrong :
= 40 - (6×2)
= 40 - 12
= 28
Score with x questions wrong :
= 40 - (x×2)
= 40 - 2x
The function f(x) = 75x + 100 models the cost of renting an event tent, where x is the number of hours and f(x) is the total cost. What is a reasonable domain for the function?
A. x < 0
B. x > 0
C. all real numbers
D. cannot be determined
Answers
The reasonable domain for the function is (b) x > 0
What is a reasonable domain for the function?From the question, we have the following parameters that can be used in our computation:
The function f(x) = 75x + 100
Where x is the number of hours
f(x) is the total cost.
In this case, the number of hours cannot be negative or 0
This means that the values of x in the function would be x > 0
These values of x are the domain
So, the reasonable domain for the function os (b) x > 0
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A student measures the mass of a sample is 2.7 grams. What is the percent error, given that the correct mass is 2.58 grams? Round to the nearest hundredth of a percent.
Answers
Answer:
the percent error in the student's measurement is 4.65%.
Step-by-step explanation:
The percent error can be calculated using the formula:
| (measured value - actual value) / actual value | * 100%
In this case, the measured value is 2.7 grams and the actual value is 2.58 grams. Substituting these values into the formula, we get:
| (2.7 - 2.58) / 2.58 | * 100% = 4.65%
Rounding this to the nearest hundredth of a percent, we get a percent error of 4.65%.
Therefore, the percent error in the student's measurement is 4.65%.
A golfer aims for a hole that is 120 feet away and, when he hits the golf ball off the ground, its highest point reaches 80 feet up in the air. Noemi’s team is working together to write the quadratic equation to model the path of the golf ball in graphing form. She calculated the value of a = - 1/90 . Is she correct?
Answers
Answer:
No she isn't. The value of \(a\) is \(a=-\frac{1}{45}\)
Step-by-step explanation:
We know that all quadratic equation can be written in the following way :
\(y=ax^{2}+bx+c\) (I)
Where \(a,b\) and \(c\) are real numbers.
I will attach a drawing with the quadratic graph to understand the situation.
We know by looking at the drawing and analyzing it that the parabola passes through the points : \((0,0) ; (60,80)\) and \((120,0)\)
\((0,0)\) because we put our coordinates origin there.
\((120,0)\) because that's where the golf hole is.
And \((60,80)\) because we know that its highest point reaches 80 feet up in the air at the middle of the distance between its roots (property of a negative parabola).
Finally, we work with the three points and the equation (I) in order to find the values of \(a,b\) and \(c\) ⇒
The parabola passes through \((0,0)\) ⇒
\(y=ax^{2}+bx+c\) ⇒
\(0=a(0)^{2}+b(0)+c\) ⇒ \(c=0\)
The parabola passes through \((60,80)\) ⇒
\(80=a(60)^{2}+b(60)\) ⇒
\(80=3600a+60b\) (II)
The parabola passes through \((120,0)\) ⇒
\(0=a(120)^{2}+b(120)\) ⇒
\(0=14400a+120b\)
\(120b=-14400a\)
\(b=-120a\) (III)
Now if we use (III) in (II) ⇒
\(80=3600a+60(-120a)\)
\(80=3600a-7200a\)
\(3600a=-80\)
\(a=-\frac{1}{45}\) ⇒ \(b=\frac{8}{3}\)
Finally the equation of the parabola is
\(y=-\frac{x^{2}}{45}+\frac{8}{3}x\)
Where the value of \(a\) is \(a=-\frac{1}{45}\)
