Question

What is y=-x^2-14x-59 in vertex form

Answer 1

The equation of a parabola given $y=-x^2-14x-59$

We have to write it in vertex form.

The vertex form of a parabola is $y=a(x-h)^2+k$

So to write it in vertex form we have to make the right side as a perfect square by using completing the square method.

$y= -x^2-14x-59$

$y=-(x^2+14x+59)$

Here 14x given. By dividing 14 by 2 we will get 7. So we have to add and subtract $(7)^2$ to the right side.

$y= -[x^2+14x+(7)^2-(7)^2+59]$

$y=-[x^2+14x+(7)^2-49+59]$

We know that, $a^2+2ab+b^2 = (a+b)^2$, so $x^2+(2)(x)(7)+7^2 = (x+7)^2$.

$y= -[(x+7)^2-49+59]$

$y=-[(x+7)^2 +10]$

$y=-(x+7)^2-10$

So we have got the required vertex form of the parabola.