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We have spent a lot of time looking at how to use algebra to factorise and solve quadratics. We have completed the square, we have used the quadratic equation and we have used the T-Method. This has led to this series of videos where we now use all the information gained to sketch the graphs. We need to make sure that, for all quadratics, we have access to tools to find the x-intercepts, y-intercepts and the turning point. Once we have these four pieces of information we can confidently sketch any quadratic equation. In this video we recap how to use the T-Method to factorise. There are a number of examples in how to solve the quadratic and find the important points. The video is a little long, but it covers all the things you need to know.
This video is the second in a series of videos which show how to sketch parabolas. This video looks at recapping the work on completing the square. Knowing how to complete the square means we can use the turning point form to find the turning point. This also allows us to solve equations to find the x-axis intercepts. I explain how the knowledge of DOPS and completing the square lets us know if we can find solutions to equations. I also look at how completing the square form can also allow us to find the y-axis intercepts. We can sketch any quadratic if we know four key pieces of information: * Turning point * y-axis intercept * Two x-axis intercepts. There are some practical examples and all the theory is fully explained. I hope the video is useful to people!
This video is freaking awesome (if I do say so myself!). It looks at how we can find the points of intercepts between a line and a curve. In this case, the curves we are looking at are parabolas and the lines are all straight lines. Starting by looking at simultaneous equations we look at how we can use Maths to find the point of intersection by solving simultaneous equations using either substitution or elimination. And I know that lots of people will be groaning here! This is extended to look at how we can find the points of intersection using DESMOS for a straight line and a curve (parabola). We look at what it means to solve a quadratic and draw a conclusion about how this is really finding the points of intersection between a curve and the line y=0. Once this has been done we look at examples using algebra by sketching parabolas and then drawing straight lines. We find the points of intersection before moving on to looking at the discriminant and how this helps us find the number of points of intersection of a line and a parabola. Such fun!
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These are the videos which are available in each chapter. You will notice that some are free and some are for subscribers only. Making and hosting these videos costs a little bit of money. To help pay for the hosting fees I have no choice but to hide some of the videos and make them for subscribers only.