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F(x) = 5x2 – 20x + 26
In vertex form

User Opher
by
4.8k points

1 Answer

6 votes

Answer:


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)

User Sebastian Vom Meer
by
4.9k points