Question

For the function f defined by f(x)=ax^2−15, where a is a constant and f(3)=10, which of the following is equal to the value of f(5)?

a. 5a−40
b. 25a−40
c. 10a−15
d. 20a−15

Answer 1

After finding the constant a from the given f(3)=10, we substitute x=5 into the equation f(x)=ax^2-15 to get f(5)=25a-40. Hence, f(5) equals 110 which matches option b.

Step-by-step explanation:

The student asked for the value of f(5) given a function f(x)=ax^2−15, where a is a constant, and f(3)=10. To find the value of a, first substitute x with 3 in the function: 10 = a(3)^2 - 15. Solving for a gives a = 5. Now, substitute x with 5 and a with 5 into the function to find f(5): f(5)=5(5)^2−15, which simplifies to 125 - 15, and further simplifies to 110. Therefore, the value of f(5) is 110, which corresponds to option b, 25a−40.