An inequality is used to show that one expression may not be equal to another.

A quadratic is an equation, graph or sequence where the highest exponent of the variable is 2. The general form for a quadratic is ax^2 + bx + c

Solving quadratic inequalities in one variable graphically

Maths

In this unit, pupils will learn how to extend their understanding of solving equations and extend this to consider inequalities. Pupils will consider a variety of inequalities and ways that their solutions can be represented.

Inequalities

$$-5<x<5$$ is the __________ the quadratic inequality $$x^2-25<0$$.

This is the curve $$y=x^2-9$$ Use the graph to solve $$x^2-9<0$$.

This is the curve $$y=x^2-9$$. Use the graph to solve $$x^2-9>0$$.

This is the curve $$y=x^2-9$$. Use the graph to solve $$x^2-9<-9$$.

This is the curve $$y=x^2-4x+4$$. The solution to the inequality $$1<x^2-4x+4<4$$ is $$0<x<1$$ or {{}}.

Rearrange and sketch to solve $$100-x^2<64$$.

When graphed, a quadratic equation forms...

This could be the sketch of which one of these quadratics?

What is the minimum value of this quadratic?

The solution to $$2x^2-14=x^2-3x+14$$ is $$x=4$$ and $$x=$${{}}.

This lesson will be removed by end of Summer Term 2025.

Solving quadratic inequalities in one variable graphically

Lesson outcome

This lesson will be removed by end of Summer Term 2025.