# What is the the vertex of y =-x^2-12x-14 ?

Jan 3, 2016

Complete the square to find the vertex.

#### Explanation:

y = -${x}^{2}$ - 12x - 14
y = -(${x}^{2}$ + 12x) - 14
y = -(${x}^{2}$ + 12x + n - n) - 14
n = ${\left(\frac{b}{2}\right)}^{2}$
n = ${\left(\frac{12}{2}\right)}^{2}$
n = 36
y = -(${x}^{2}$ + 12x + 36 - 36) - 14
y = -(${x}^{2}$ + 12x + 36) + 36 - 14
y = -${\left(x + 6\right)}^{2}$ + 22

In the form y = a${\left(x - p\right)}^{2}$ + q, the vertex is at (p, q)

So, the vertex of $- {x}^{2}$ - 12x - 14 is (-6, 22).

Hopefully you understand now