Question

The following table shows the revenue a company generates based on the increases in the price of
the product.

Number of $2 increases in price
3
5
7
9
Revenue
1045
1105
1125
1105
1045'

What is the equation of the quadratic that models the data?

Answer 1

To find the equation of the quadratic that models the data, we can use the general form of a quadratic equation:

y = ax^2 + bx + c

We can substitute the values from the table into the equation to form a system of equations:

1045 = a(3)^2 + b(3) + c
1105 = a(5)^2 + b(5) + c
1125 = a(7)^2 + b(7) + c

This gives us the following system of equations:

9a + 3b + c = 1045
25a + 5b + c = 1105
49a + 7b + c = 1125

Solving this system of equations, we get:
a = -5
b = 65
c = 850

Therefore, the equation of the quadratic that models the data is:
y = -5x^2 + 65x + 850