Question

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

Answer 1

Answer:

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

Step-by-step explanation:

Answer 2

Answer:

$y=(x+4)^{2}-37$

Step-by-step 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)