Question

How do you solve the equation `2x^2=-5x+12` by graphing?

Answer 1

The intersection points occur at `(-4,32)` and `(1.5, 4.5)`.

Explanation:

There are several ways to graph this equation. One way that is popular is to graph the left hand side separately from the right and observe where they intersect with each other.

Graphing `y=2x^2` gives

graph{y=2x^2[-5,5,-5,40]}

Graphing `y=-5x+12` gives

graph{(y-2x^2)(y+5x-12)=0[-5,5,-5,40]}

The intersection points occur at `(-4,32)` and `(1.5, 4.5)`.

One very easy way to see these is to plot both equations in Desmos.com, which gives the following interactive graph.