Question

f(x) = 5x2 – 20x + 26
In vertex form

Answer 1

Answer:

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

Step-by-step 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)