# How do you graph y=x^2+8-3x?

Jun 25, 2018

Here's one way: complete the square to find its vertex, then calculate a few more points by plugging in values of $x$.

#### Explanation:

Let's rearrange the equation:
$y = {x}^{2} - 3 x + 8$

This equation can't be factored, so let's complete the square:
$y = \left({x}^{2} - 3 x + \frac{9}{4} - \frac{9}{4}\right) + 8$
$y = {\left(x - \frac{3}{2}\right)}^{2} - \frac{9}{4} + 8$
$y = {\left(x - \frac{3}{2}\right)}^{2} + \frac{23}{4}$

This is the equation in vertex form: $y = a {\left(x - h\right)}^{2} + k$
We know the vertex is $\left(h , k\right) = \left(\frac{3}{2} , \frac{23}{4}\right) .$

The leading coefficient $a$ is positive, which means that the parabola opens upwards.

We can get a few more points of the parabola by plugging in some values of $x$ around $\frac{3}{2}$.

Substituting $x = 2$, we find $\left(2 , 6\right)$.
Substituting $x = 1$, we find $\left(1 , 6\right)$.
Substituting $x = \frac{5}{2}$, we find $\left(\frac{5}{2} , \frac{27}{4}\right)$.
Substituting $x = \frac{1}{2}$, we find $\left(\frac{1}{2} , \frac{27}{4}\right)$.

Graph and connect these points. Be sure to label the equation of the graph, label the axes, and include arrowheads.