# Quadratic Inequalities | Algebra | Maths for All | FuseSchool

CREDITS
Animation & Design: Jean-Pierre Louw – www.behance.net/Appel718
Narration: Lucy Billings
Script: Lucy Billings

You probably already know that quadratic equations look like this… We can also have quadratic inequalities… We use inequalities to show us a range of possible
values… which actually has many real life uses.

For example, I might use them to work out that I need to film a racecar between 10 and 15 seconds after the start of the race. And they’re used throughout finance, such as working out what loan you can afford based on your
expenditure.

We solve quadratic inequalities in pretty much the same way we solve quadratic equations, but also making use of the graph to help us work out which part we want… let’s have a look at an example. Solve it like you normally would… so factorise, quadratic formula or complete the square. This one factorises.

Notice how i’ve changed it to be equals now. Solve each bracket, x equals 3 and x equals negative 2. Sketch what this quadratic looks like… U shaped, crossing the x-axis at -2 and 3. It’s just a rough sketch to help yourself in answering the question, so don’t worry too much about it at all. Because we want where the quadratic is LESS THAN zero. We want this part of the graph – the part that is less
than 0 for y but also has the quadratic in.

This means the answer is x is greater than or equal to negative 2 but less than or equal to 3. Because we’ve shaded one joined region, the answer is one inequality.
It’s this inequality sign because that was in the question.

Because we have 2 separate regions shaded, this means we have 2 separate inequality answers. Where x is less than negative 4 And where x is greater than negative 2. Because the question was a “greater than” inequality, that’s what our answers are…No “or equal to” involved. And that’s all there is to solving quadratic
inequalities. You just need to do a little sketch of the graph, and work out the values from there.

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