# How to graph a parabola y=x^(2)-2x-15?

##### 1 Answer
Jun 21, 2018

You have two choices
1. complete the square to get standard form, find vertex and 2 other points.
2. Use the equation $x = \left(- \frac{b}{2} a\right)$ to find the x-coordinate of the vertex.

#### Explanation:

Complete the square...
$y = \left({x}^{2} - 2 x + {\left(\frac{b}{2}\right)}^{2}\right) - 15 - {\left(\frac{b}{2}\right)}^{2}$
$y = \left({x}^{2} - 2 x + 1\right) - 15 - 1$
$y = {\left(x - 1\right)}^{2} - 16$ so the vertex is at (1, -16)
find two more points, use x-values near the vertex.
(0, -15) and by symmetry (2, -15) and (-1, -12).

Alternatively,
Use $h = \left(- \frac{b}{2} a\right)$ for the x-coordinate of the vertex
and $k =$ the y-value when you substitute x = h into the equation.
write as $y = a {\left(x - h\right)}^{2} + k$ here a=1, the vertex is (h, k).
You need to calculate 2 more points as above.