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Find the minimum y-value on the graph of y=f(x)

F(x) = 7x^2 + 7 - 6

Find the minimum y-value on the graph of y=f(x) F(x) = 7x^2 + 7 - 6-example-1
User Malclocke
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1 Answer

4 votes

Answer:

The minimum y-value is


y=-(31)/(4) or
y=-7.75

Explanation:

we have


f(x)=7x^(2)+7x-6

This is the equation of a vertical parabola open up

The vertex is the minimum y-value on the graph

Convert the equation into vertex form

Group terms that contain the same variable, and move the constant to the opposite side of the equation


f(x)+6=7x^(2)+7x

Factor the leading coefficient


f(x)+6=7(x^(2)+x)

Complete the square. Remember to balance the equation by adding the same constants to each side


f(x)+6+1.75=7(x^(2)+x+0.25)


f(x)+7.75=7(x^(2)+x+0.25)

Rewrite as perfect squares


f(x)+7.75=7(x+0.5)^(2)


f(x)=7(x+0.5)^(2)-7.75 ------> equation in vertex form

The vertex is the point (-0.5,-7.75)

therefore

The minimum is the point (-0.5,-7.75)

The minimum y-value is
y=-7.75=-7(3)/(4)=-(31)/(4)

see the attached figure to better understand the problem

Find the minimum y-value on the graph of y=f(x) F(x) = 7x^2 + 7 - 6-example-1
User Thefreeman
by
6.7k points