Example 2

Example 1

# Sketching Quadratics

## Why we Sketch Quadratics

We sketch quadratics to graphically represent a quadratic equation. It’s the same
as graphing linear functions just that we end up with a parabola instead of a straight
line.
## Sketching Quadratics

In the example underneath, we have sketch the quadratic y=x²-x-2. The first step is to let x = 0. Just replace every x value in the quadratic by 0 and you
will get y=n. Then write this as a co-ordinate (0,n). Next you let y=0 which allows you to solve the quadratic. You then put the answer(s) to the quadratic
in co-ordinate form too: (a,0) and (b,0). Then plot the points on a graph. Locate the point between the two points where the line will cross the x-axis. This
is the axis of symmetry. Now draw the parabola going through the x and y values we found. The parabola should turn (have its lowest point) exactly
where the axis of symmetry is.

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## Special Cases

If the quadratic is negative, the parabola will be the other way around. It is also possible that the parabola
crosses the y-axis before crossing the x-axis. Both of these cases are shown in the graph on the right.
## Mastering Quadratics

You should now know hot to solve quadratic using different methods and how to sketch them on a graph. We recommend that you have
a look at inequalities next or you can select another topic in our library. Please share this page if you like it or found it helpful!

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Chapter 17.4: Learning Outcomes
Students will learn how to sketch quadratics!
Students will learn about special cases when sketching quadratics!

## VIDEO LESSON:

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