Question

Use the method of completing the square to write the equations of the given parabola in this form: (y-k)=a(x-h)^2 where a =0, (h,k) is the vertex, and x=h is the axis of symmetry. Find the vertex of this parabola: y=-4x^2-8x-7

Answer 1

(-1, -3)

Explanation:

`(y-k)=a(x-h)^2,\ a\\eq0`

`(a\pm b)^2=a^2\pm2ab+b^2\qquad(*)`

We have

`y=-4x^2-8x-7`

`y=-4x^2-4(2x)-4(1)-3`

distribute

`y=-4(\underbrace{x^2+2x+1}_((*)))-3`

use (*)

`y=-4(x+1)^2-3`

add 3 to both sides

`y+3=-4(x+1)^2`

`y-(-3)-4\bigg(x-(-1)\bigg)^2`

the vertex

`(-1;\ -3)`