# How do you write y=x^2+16x+14 in vertex form?

How do you write $y={x}^{2}+16x+14$ in vertex form?
You can still ask an expert for help

• Questions are typically answered in as fast as 30 minutes

Solve your problem for the price of one coffee

• Math expert for every subject
• Pay only if we can solve it

Jordan Mitchell
By completing the square:
$y={x}^{2}+16x+{\left(\frac{16}{2}\right)}^{2}-{\left(\frac{16}{2}\right)}^{2}+14$
$y={\left(x+8\right)}^{2}-64+14$
$y={\left(x+8\right)}^{2}-50$
###### Not exactly what you’re looking for?
vicki331g8
Complete the square for ${x}^{2}+16x+14$
Use the form $a{x}^{2}+bx+c$, to find the values of $a,b,$ and c.
Consider the vertex form of a parabola.
$a{\left(x+d\right)}^{2}+e$
Substitute the values of a and b into the formula $d=\frac{b}{2a}$
$d=\frac{16}{2\left(1\right)}$
Cancel the common factor of 16 and 2.
$d=8$
Find the value of e using the formula $e=c-\frac{{b}^{2}}{4a}$
$e=-50$
Substitute the values of $a,d$ and e into the vertex form $a{\left(x+d\right)}^{2}+e$
${\left(x+8\right)}^{2}-50$
Set y equal to the new right side.
$y={\left(x+8\right)}^{2}-50$