Question

A quadratic function is defined by:

f(x) = x^2 - 8x - 4.
Rewrite this into vertex form by completing the square to reveal the vertex (minimum) of the function. What is the vertex (minimum)?

A) (4, -20)
B) (-4, 20)
C) (4, 20)
D) (-4, -20)

Answer 1

To rewrite the quadratic function into vertex form, complete the square by isolating the terms with x and adding/subtracting the square of half of the coefficient of x. The vertex is (4, -20).

Step-by-step explanation:

To rewrite the quadratic function f(x) = x^2 - 8x - 4 into vertex form, we need to complete the square. The vertex form of a quadratic function is given by f(x) = a(x - h)^2 + k. To find the vertex, we first need to find the values of h and k. Start by isolating the terms with x: f(x) = (x^2 - 8x) - 4. We can complete the square by adding and subtracting the square of half of the coefficient of x: f(x) = (x^2 - 8x + 16) - 16 - 4. Simplifying, we get: f(x) = (x - 4)^2 - 20. Therefore, the vertex is (4, -20).