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 given points:
(1, 1045), (3, 1105), (5, 1125), (7, 1105), (9, 1045)
We can start by writing the general form of a quadratic equation:
y = ax^2 + bx + c
Next, we can substitute the points into the equation:
1045 = a(1)^2 + b(1) + c
1105 = a(3)^2 + b(3) + c
1125 = a(5)^2 + b(5) + c
1105 = a(7)^2 + b(7) + c
1045 = a(9)^2 + b(9) + c
Solving these equations, we find a = -5, b = 0, and c = 1125.
Therefore, the equation of the quadratic that models the data is:
y = -5x^2 + 1125
The answer is not among the options provided.