Question

F(x) = 5x2 – 20x + 26
In vertex form

Answer 1

`f(x)=5(x-2)^(2)+6`

Explanation:

we have

`f(x)=5x^(2) -20x+26`

This is the equation of a vertical parabola open upward

The vertex is a minimum

The equation of a vertical parabola in vertex form is equal to

`f(x)=a(x-h)^2+k`

where

(h,k) is the vertex

Convert the given function to vertex form

Factor the leading coefficient

`f(x)=5(x^(2) -4x)+26`

Complete the square

`f(x)=5(x^(2) -4x+4)+26-20`

`f(x)=5(x^(2) -4x+4)+6`

Rewrite as perfect squares

`f(x)=5(x-2)^(2)+6` ------> equation in vertex form

The vertex is the point (2,6)