Question

Find the vertex of y = x^2 – 2x – 15

Answer 1

The vertex is at (h, k), which here is (1, -16).

Explanation:

One of the quicker ways to approach this proplem is to "complete the square," which puts the equation into "vertex form."

Starting with y = x^2 – 2x – 15, add 1 to, and then subtract 1 from, x^2 – 2x :

y = x^2 – 2x + 1 - 1– 15

Now re-write x^2 – 2x as (x - 1)^2 - 1:

y = (x - 1)^2 - 1 – 15. or y = (x - 1)^2 - 16, which has the form y = (x - h)^2 + k. Comparing these two equations, we see that h = 1 and k = -16.

The vertex is at (h, k), which here is (1, -16).

Answer 2

The vertex is ( 1, -16 ).