Question

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

Answer 1

`y+6=(x+1)^(2)`

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)