Roots of a Quadratic on a Graph

Today we find where a parabola crosses the x-axis—those are the roots. A quadratic function is y equals a x squared plus b x plus c.

The roots are the x values where y equals zero—where the curve touches the x-axis. Let's use a concrete example: y equals x squared minus five x plus six.

• Roots: where y = 0

I'll draw this parabola on a graph. See where the curve crosses the x-axis? That happens at x equals two and x equals three. So the roots are x equals two and x equals three.

• Roots: x = 2 and x = 3

We can check: plug in x equals two. Two squared minus five times two plus six equals zero. Yes!

And plug in x equals three. Three squared minus five times three plus six equals zero. Also yes!

The vertex—the lowest point—sits exactly halfway between the two roots. A parabola can have two roots, one root, or no real roots at all. Quick check: which x value is a root of y equals x squared minus four?

• Vertex x-value: (2+3)/2 = 2.5
• Two roots, one root, or none

The roots are where the parabola meets the x-axis, and you can always read them straight off the graph.

• Read roots from graph