To determine the equation of the quadratic that models the data, we need to find the vertex form of a quadratic equation. In this case, the vertex form is given by:
y = a(x-h)^2 + k
Where (h, k) is the vertex of the parabola.
From the data provided, we can see that the maximum revenue occurs when the price increases by 7 times $2, resulting in a revenue of $1125. This gives us the vertex point (7, 1125).
Plugging the vertex point into the vertex form, we get:
y = a(x-7)^2 + 1125
To find the value of 'a' we can use another data point, such as the revenue of $1105 when the price increases 5 times $2. Plugging this point into the equation, we get:
1105 = a(5-7)^2 + 1125
1105 = 4a + 1125
-20 = 4a
a = -5
Therefore, the equation of the quadratic that models the data is:
y = -5(x-7)^2 + 1125
This simplifies to:
y = -5(x^2 - 14x + 49) + 1125
y = -5x^2 + 70x - 245 + 1125
y = -5x^2 + 70x + 880
So, the correct answer is:
d. y = -5(x-7)^2 + 1125
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?
c. y=-5(x+5)^2-1125
d. . y=-5(x-5)^2+1125
explain how you solved it
1 answer