Question

What is the vertex of the quadratic function f(x) = (x – 6)(x + 2)?

Answer 1

Answer:

The vertex is (2,-16)

Step-by-step explanation:

The given function is $f(x)=(x-6)(x+2)$

We expand to obtain;

$f(x)=x^2+2x-6x-12$

$f(x)=x^2-4x-12$

We complete the squares to obtain;

$f(x)=x^2-4x+(-2)^2-12-(-2)^2$

$f(x)=x^2-4x+(-2)^2-12-4$

$f(x)=(x-2)^2-16$

The vertex form is $f(x)=(x-2)^2-16$

Comparing this to

$f(x)=a(x-k)^2+k$

The vertex is (h,k)= (2,-16)