 Quadratics, those little equations with an x squared in, you should know that when they're graphed, if they're a positive x squared, they'll look like this, and if they're a negative x squared, they'll look like this. In this video, we're going to discover how the equation of quadratic matches up to the graph of the quadratic. So we'll be able to connect the solutions from factorizing to the graph and we'll also be able to find the y-intercept. In part two, we're going to look at the turning points and the axes of symmetry of the quadratic. So there's a few things to discover about the graphs of quadratic, beyond the fact that they're either u-shaped or n-shaped. Before we get started, another name for the solutions are roots. So three and negative one are the roots of this quadratic. So let's jump straight in and have a look at the graph. What do you notice about the roots when factorized and where the graph crosses the x-axis? I'm sure that you spotted that when you factorize a quadratic, the roots are exactly where the quadratic function crosses the x-axis. This information is really helpful when sketching a quadratic. What do you notice about the y-intercept and the equation of the quadratic? Did you spot that the number on its own in the equation is the y-intercept? So straight away when we have a quadratic equation, we already know what shape it is, so positive x squared is a smiley u-shape and a negative x squared is a sad n-shape. And we can really easily work out three points on its graph without having to draw it using a table of values, the y-intercept and the 2x-intercept. This means we can do a really quick sketch and label some values, so the sketch for y equals x squared plus 2x minus 8 would look something like this. Because negative 8 in the equation gives us the y-intercept and factorizing the quadratic gives the roots negative 4 and 2. So here's two for you to do, sketch the quadratics giving the correct shape and labeling three points on the axis. Watch out for the negative quadratic, pause the video, sketch the quadratics and click play when you're ready to check. You should have sketches that look something like these, with these values marked on. So there we have sketching quadratics making use of the roots and the y-intercept. In the next video we'll also look at the turning points so the maximum or minimum point on the quadratic. They make use of the fact that quadratics are symmetrical, so we'll also discover what the axis of symmetry is.