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Neko [114]
3 years ago
8

What is the y-value if the vertex of 4x^2 + 8x - 8

Mathematics
2 answers:
Levart [38]3 years ago
6 0

The x-value is -b/(2a) = -8/(2·4) = -1.

The corresponding y-value is ...

... 4(-1)² +8(-1) -8 = 4 -8 -8 = -12

The y-value of the vertex is -12.

djverab [1.8K]3 years ago
5 0

Answer:

The y-value of the vertex is -12

Step-by-step explanation:

we know that

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

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

where

(h,k) is the vertex of the parabola

In this problem we have

f(x)=4x^{2}+8x-8 -----> this a vertical parabola open upward

Convert to vertex form

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

f(x)+8=4x^{2}+8x

Factor the leading coefficient

f(x)+8=4(x^{2}+2x)

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

f(x)+8+4=4(x^{2}+2x+1)

f(x)+12=4(x^{2}+2x+1)

Rewrite as perfect squares

f(x)+12=4(x+1)^{2}

f(x)=4(x+1)^{2}-12

The vertex is the point (-1,-12)

The y-value of the vertex is -12


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