How do you write the Vertex form equation of the parabola y=x^2 - 9x?

Jun 19, 2017

The vertex form is ${\left(x - 4.5\right)}^{2} + 20.25$.

Explanation:

$y = {x}^{2} - 9 x$ is the standard form for a parabola: $a {x}^{2} + b x + c$, where $a = 1$, $b = - 9$, and $c = 0$.

The vertex form is $y = a {\left(x - h\right)}^{2} + k$, where $h = \frac{- b}{2 a}$ and $k = f \left(h\right)$

$h = \frac{- \left(- 9\right)}{2 \cdot 1} = 4.5$

Substitute the value of $h$ for $x$ into the standard form.

$k = f \left(h\right) = {\left(4.5\right)}^{2} - 9 \left(4.5\right) = - 20.25$

Vertex form is ${\left(x - 4.5\right)}^{2} + 20.25$