# The graph of y=x^2-6x+k as its vertex on the x-axis. How do you find the value of k?

Nov 23, 2016

Set y = 0, evaluate the quadratic at $h = - \frac{b}{2 a}$ and solve for k.
$k = 9$

#### Explanation:

You want the to find the value of k such that the y coordinate of the vertex is 0.

$0 = {x}^{2} - 6 x + k$

The x coordinate, h, of the vertex is found, using the following equation:

$h = - \frac{b}{2 a}$

$h = - - \frac{6}{2 \left(1\right)} = 3$

Evaluate at x = 3:

$0 = {3}^{2} - 6 \left(3\right) + k$

$k = 9$