Question

Rewrite the equation of the parabola in vertex form. y= x2 + 8x - 21

Answer 1

the answer is y=(x+4)^2-37

Explanation:

Answer 2

`y=(x+4)^(2)-37`

Explanation:

we know that

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

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

where

(h,k) is the vertex of the parabola

if a> 0 then the parabola open upward (vertex is a minimum)

if a< 0 then the parabola open downward (vertex is a maximum)

In this problem we have

`y=x^(2)+8x-21`

Convert to vertex form

Complete the square

`y+21=x^(2)+8x`

`y+21+16=(x^(2)+8x+16)`

`y+37=(x^(2)+8x+16)`

`y+37=(x+4)^(2)`

`y=(x+4)^(2)-37` --------> equation in vertex form

The vertex is the point
`(-4,-37)`

the parabola open upward (vertex is a minimum)