 In an earlier video, we discovered that the roots of a quadratic give us the x-axis intercepts and the number on its own in a quadratic gives us the y-intercept. We also know that a positive x-squared gives us a smiley u-shape and a negative x-squared gives us a sad n-shape curve. We can really easily sketch a quadratic like this. In this video, we're going to discover even more information connecting the quadratic equation with its graphed function. We will look at the turning points, so the maximum and minimum. These are also known as the vertex. Quadratic functions are symmetrical. They have a line of symmetry, which is known as the axis of symmetry. The turning point will always sit on the axis of symmetry. In a positive quadratic, the turning point is a minimum. It's the lowest point of the function. And in a negative quadratic, the turning point is a maximum. It's the highest point of the function. We can easily find the x-coordinate of the turning point by using this simple little equation. So B is the value in front of the x in the equation and the A is the value in front of the x-squared. So let's check it for this graph. A is 1 and B is negative 2. So the axis of symmetry equals minus negative 2 divided by 2 multiplied by 1. So 2 divided by 2, which is 1, so x equals 1. Can you find the axis of symmetry for this quadratic? Pause the video, work out the answer and click play when you're ready. Did you get x is negative 2 as the line? Why stop there? We can find out the y-coordinate of the turning point, not just the line of symmetry. We use our x-value from the axis of symmetry and just substitute that into the original quadratic equation. So the coordinates of the turning point are 1, negative 4. So what is the coordinate of this turning point and is it a minimum or a maximum? Pause the video, work out the answer and click play when you're ready to check. Did you get the minimum at 2, negative 16? So that's the final piece of the sketching quadratic's puzzle. Let's now combine all of our knowledge about the x-axis intercepts, the y-intercept, the shape, and the coordinates of the turning points. If you've forgotten about the roots and the y-intercept, you may want to watch this video first. Otherwise, give this question a go, sketching the quadratic and labelling on four points onto the graph. Pause the video, sketch the quadratic and click play when you're ready to check. How did you get on? So that's the axis of symmetry, which we use to find the coordinates of our turning point. We have this little formula which we use and just have a look on your formula sheet or check with your teacher because you are normally given it, but you may need to memorize it. Once we have the x-value, we just substitute that into our original quadratic equation to find the y-coordinate. 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 Fusco app as well? Until next time!