Question

A quadratic function is defined by f(x) = x^2 - 8x - 4 Which expression also defines f and best reveals the maximum or minimum of the function?

Answer 1

Answer: D

Explanation:

(x-4)²-20

(x-4)(x-4)-20

(x^2)-8x+16-20

= (x^2)-8x-4

D is the same equation as in the question, just written in another form (they are equal). In this form (vertex), the vertex is (h,k), which is easily found in this equation. The vertex reveals the maximum or minimum. The vertex in this problem is (4,-20) because vertex form is f(x)=a(x-h)^2 + k.

Answer 2

The quadratic function f(x) = x^2 - 8x - 4 can be rewritten in vertex form as f(x) = (x - 4)^2 - 20, where the vertex is at (4, -20). Since the coefficient of the x^2 term is positive, the parabola opens upwards and the vertex represents the minimum value of the function. Therefore, the expression that also defines f and best reveals the maximum or minimum of the function is f(x) = (x - 4)^2 - 20. should be right