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.

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!



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