Question

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

Answer 1

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)