Question

What are the coordinates of the vertex of the function f(x) = x2 - 12x + 5?

Answer 1

Answer:

The vertex is the point (6,-31)

Step-by-step explanation:

we have

$f(x)=x^2-12x+5$

This is a vertical parabola open upward

The vertex represent a minimum

Convert to vertex form

Complete the square

$f(x)=(x^2-12x+6^2)+5-6^2$

$f(x)=(x^2-12x+36)-31$

Rewrite as perfect squares

$f(x)=(x-6)^2-31$ -----> equation in vertex form

therefore

The vertex is the point (6,-31)