Question

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

Answer 1

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 = `(b/2)^2`
n = `(12/2)^2`
n = 36
y = -(`x^2` + 12x + 36 - 36) - 14
y = -(`x^2` + 12x + 36) + 36 - 14
y = -`(x + 6)^2` + 22

In the form y = a`(x - p)^2` + q, the vertex is at (p, q)

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

Hopefully you understand now