 You probably already know that quadratic equations look like this, but we can also have quadratic inequalities. We use inequalities to show us a range of possible values, which actually have many real-life uses. For example, I might use them to work out that I need to film a race car between 10 and 15 seconds after the start of a 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. So 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 become equals. Solve each bracket, so x equals 3 and x equals negative 2. Sketch what this quadratic looks like. This u-shaped crossing the x-axis at negative 2 and 3. It's just a rough sketch to help yourself in answering the question, so don't worry about it too much. Because we want where the quadratic is less than zero, we want this part of the graph, the part that is less than zero 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. Here's another example. Start by solving it. Roughly sketch the quadratic. Now, we want where the quadratic is more than zero. So shade where the quadratic is more than zero. This time, because we have two separate regions shaded, this means we have two separate inequality answers. Where x is less than negative 4 and where x is greater than negative 2. Because the question was greater than inequality, that's what our answers are. There's no or equals to involved. Here's two for you to do. Pause the video, solve the inequalities and click play when you're ready. How did you get on? You just need to do a quick sketch of the quadratic and then work out the values from there. If you have any questions, comment below and I'll answer them for you. Like and share our videos with your friends. If you liked the video, give it a thumbs up and don't forget to subscribe. Comment below if you have any questions. Why not check out our Fuse school app as well. Until next time.