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.