8
AssignmentMultiple Choice

Modeling with Quadratic Functions

Question 8 • *Integrated Math II Full

An image of a parabolic lens is projected onto a graph. The y-intercept of the graph is (0, 90), and the zeros are 5 and 9. Which equation models the function?

Answer
A
y = 90(x – 5)(x – 9)
B
y = 2(x – 5)(x – 9)
C
y = 90(x + 5)(x + 9)
D
y = 2(x + 5)(x + 9)

Explanation

Since the zeros are 5 and 9, the function has the form y = a(x − 5)(x − 9). Use the y-intercept (0, 90): substituting x = 0 gives 90 = a(−5)(−9) = 45a, so a = 2. Therefore, the equation is y = 2(x − 5)(x − 9), choice B.

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