How do you convert y=x^2+18x+95 in vertex form?

Mar 15, 2018

$y = {\left(x + 9\right)}^{2} + 14$

Explanation:

First find the vertex using the formula
$x = \frac{- b}{\text{2a}}$

$a = 1$
$b = 18$
$c = 95$

$x = \frac{- \left(18\right)}{\text{2(1)}}$ This simplifies to $x = - \frac{18}{\text{2}}$ which is $- 9$.
so $x = - 9$

So on now that we have $x$ we can find $y$.

$y = {x}^{2} + 18 x + 95$
$y = {\left(- 9\right)}^{2} + 18 \left(- 9\right) + 95$
$y = 14$

Vertex = $\left(- 9 , 14\right)$ where $h = - 9$ and $k = 14$

We now finally enter this into vertex form which is,
$y = a {\left(x - h\right)}^{2} + k$

$x$ and $y$ in the "vertex form" are not associated with the values we found earlier.

$y = 1 {\left(x - \left(- 9\right)\right)}^{2} + 14$
$y = {\left(x + 9\right)}^{2} + 14$

Mar 15, 2018

${\left(x + 9\right)}^{2} + 14$

Explanation:

Firstly, you have to find the vertex point. Use the formula ${x}_{v} = - \frac{b}{2 a}$. You get $\left(h\right) {x}_{v} = - 9$ and $\left(k\right) {y}_{v} = 14$

Since there's an imaginary 1 in front of x, the a value is 1.
Now just plug everything into the equation $y = a {\left(x - h\right)}^{2} + k$