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skad [1K]
3 years ago
14

Convert y = x^2 + 2x - 5 into the form y-k = a( x- h)^2

Mathematics
1 answer:
leva [86]3 years ago
7 0

Answer:

y+6=(x+1)^{2}

Step-by-step explanation:

we have

y=x^{2}+2x-5

This is the equation of a vertical parabola open upward (because the leading coefficient is positive)

The vertex is a minimum

The equation of a vertical parabola into vertex form is

y-k=a(x-h)^2

where

(h,k) is the vertex of the parabola

Convert the equation into vertex form

Move the constant term to the left side

y+5=x^{2}+2x

Complete the square

y+5+1=x^{2}+2x+1

y+6=x^{2}+2x+1

Rewrite as perfect squares

y+6=(x+1)^{2}

therefore

a=1\\h=-1\\k=-6

The vertex is the point (-1,-6)

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