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andriy [413]
2 years ago
10

F(x) = 5x2 – 20x + 26 In vertex form

Mathematics
1 answer:
mihalych1998 [28]2 years ago
6 0

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)

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