Number of $2 increases in price
Revenue
1
1045
3
1105
5
1125
7
1105
9
1045
What is the equation of the quadratic that models the data?
A) y=(x+5)^2-1125
B) y=(x-5)²+1125
C) y = -5(x+5)² - 1125
D) y = -5(x-5)² + 1125
To find the equation of the quadratic that models the data, we can create a system of equations using the data given.
Let's assume y = Revenue and x = Number of $2 increases in price. We can plug in the data points into the quadratic equation y = ax^2 + bx + c, where a, b, and c are coefficients we need to find.
Using the data points:
(1, 1045) gives us: 1045 = a(1)^2 + b(1) + c --> a + b + c = 1045
(3, 1105) gives us: 1105 = a(3)^2 + b(3) + c --> 9a + 3b + c = 1105
(5, 1125) gives us: 1125 = a(5)^2 + b(5) + c --> 25a + 5b + c = 1125
(7, 1105) gives us: 1105 = a(7)^2 + b(7) + c --> 49a + 7b + c = 1105
(9, 1045) gives us: 1045 = a(9)^2 + b(9) + c --> 81a + 9b + c = 1045
Now we have a system of five equations:
a + b + c = 1045
9a + 3b + c = 1105
25a + 5b + c = 1125
49a + 7b + c = 1105
81a + 9b + c = 1045
Solving this system of equations, we get:
a = -5, b = 0, c = 1125
Therefore, the equation of the quadratic that models the data is:
y = -5x^2 + 1125
The correct choice is:
B) y = -5(x-5)² + 1125