# Solving Quadratic and Linear Inequalities

In this lesson students learn about solving quadratic and linear inequalities using a sketched graph.

Later, as learning progresses students are challenged to solve a pair of quadratic inequalities.

The starter recaps solving quadratic inequalities which the students learned in the previous lesson.

To remind students of the process I demonstrate how to solve x2 – 2x – 15 > 0 by factorisation. I then sketch the graph and ask the class whether we consider the points above or below the x-axis.

Next, I ask the students to match the remaining three quadratic inequalities with there solutions.

## Solving Quadratic and Linear Inequalities

As we begin the main part of the lesson I use Autograph to quickly illustrate the two functions in question a). It is important to blank out the axis otherwise the two intersecting points are easily found.

With the axes blanked out, I ask students to work in pairs to set up and solve an equation where the two lines intersect. Having recapped the majority of this process in the starter, students have little difficulty solving the rest of the problem.

As we progress through the next few questions I continue to illustrate the graphs on Autograph so the class can solve the remainder of the problem algebraically.

## Challenge Question

The challenge question takes between 5 and 10 minutes for most students. I expect everyone to sketch the two functions on a graph and note the coordinates where each line crosses the axes. This makes it much easier to identify the points of intersection.

Some students struggle to find the roots of the quadratic given the negative -3x2 term and others drew the graph upside down. Both errors were easily addressed when feeding back on the board.

When students had correctly sketched the two functions everyone went on to finish the problem with little difficulty.

My name is Jonathan Robinson and I am passionate about teaching mathematics. I am currently Head of Maths in the South East of England and have been teaching for over 15 years. I am proud to have helped teachers all over the world to continue to engage and inspire their students with my lessons.

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