# What is the vertex form of y= x^2+8x+20 ?

Mar 11, 2018

Vertex is (-4,4 )

#### Explanation:

$y = {x}^{2} + 8 x + 20$

this can also be written as ,
y = ${x}^{2} + 8 x + {4}^{2} - {4}^{2} + 20$

which can be further simplified into,
y = ${\left(x + 4\right)}^{2} + 4$ ........ (1)

We know that,
$y = {\left(x - h\right)}^{2} + k$ where vertex is (h,k)

comparing both the equations we get vertex as (-4,4)

graph{x^2 + 8x +20 [-13.04, 6.96, -1.36, 8.64]}

Mar 11, 2018

$y = {\left(x + 4\right)}^{2} + 4$

#### Explanation:

The vertex form is: $y = a {\left(x - h\right)}^{2} + k$

when $\left(h , k\right)$ is dhe vertex of the parabola $a {x}^{2} + b x + c$

$h = - \frac{b}{2 a}$, $k = - \frac{\Delta}{4 a} = - \frac{{b}^{2} - 4 a c}{4 a}$.

Now: $y = {x}^{2} + 8 x + 20 \Rightarrow h = - \frac{8}{2} = - 4$ and $k = - \frac{64 - 4 \cdot 1 \cdot 20}{4 \cdot 1} = 4$

then the vertex form is: $y = {\left(x + 4\right)}^{2} + 4$

Second method:

$y = {x}^{2} + 8 x + 20 \Rightarrow y - 20 = {x}^{2} + 8 x \Rightarrow$

$y - 20 + 16 = {x}^{2} + 8 x + 16 \Rightarrow y - 4 = {\left(x + 4\right)}^{2} \Rightarrow$

$y = {\left(x + 4\right)}^{2} + 4$