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

1 Answer
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^2-3x+8

This equation can't be factored, so let's complete the square:
y = (x^2 - 3x + 9/4 - 9/4) + 8
y = (x - 3/2)^2 - 9/4 + 8
y = (x-3/2)^2+23/4

This is the equation in vertex form: y=a(x-h)^2+k
We know the vertex is (h,k) = (3/2, 23/4).

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 3/2.

Substituting x=2, we find (2,6).
Substituting x=1, we find (1,6).
Substituting x=5/2, we find (5/2, 27/4).
Substituting x=1/2, we find (1/2, 27/4).

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