# How do you find the vertex of a parabola y=x^2 - 9x?

Jul 18, 2015

The vertex is at color(red)((9/2,-81/4).

#### Explanation:

$y = {x}^{2} - 9 x$

The standard form of the equation for a parabola is

$y = a {x}^{2} + b x + c$, so

$a = 1$, $b = - 9$, $c = 0$

The $x$-coordinate is at x = -b/(2a) = -(-9)/(2×1) = 9/2

To find the $y$-coordinate of the vertex, substitute $x = \frac{9}{2}$ into the equation to get

y = (9/2)^2 – 9(9/2) = 81/4 – 81/2 = 81/4 – 162/4 = -81/4

The vertex is at ($\frac{9}{2} , - \frac{81}{4}$).

graph{y = x^2-9x [-10, 20, -25, 25]}

Jul 22, 2015

Another way of graphing can be as explained below.

#### Explanation:

After writing the quadratic equation in vertex form y= ${\left(x - \frac{9}{2}\right)}^{2} - \frac{81}{4}$, graphing can be done by translating the graph of y=${x}^{2}$, first horizontal shift to the right by $\frac{9}{2}$ units and then vertical shift down wards by $- \frac{81}{4}$ units