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CREDITS Animation & Design: Jean-Pierre Louw ( Narration: Lucy Billings Script: Lucy Billings In this video we are going to discover even more information connecting the quadratic equation with it’s graphed function. We will look at...\n
CREDITS Animation & Design: Jean-Pierre Louw ( Narration: Lucy Billings Script: Lucy Billings In this video we are going to discover even more information connecting the quadratic equation with it’s 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 is the lowest point of the function. And in a negative quadratic the turning point is a maximum… it is the highest point of the function. We can easily find the x-coordinate of the turning point by using this simple little equation… x = 2a −b axis of symmetry, x = 2a where −b y = ax2 + bx + c So b is the value in front of the x in the equation And a is the value in front of the x2 So let’s check it for this graph… A is 1 And b is -2 So the axis of symmetry = - -2 / 2 X 1 So 2 / 2 which is 1. So x = 1 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, -4) So that’s the final piece of the puzzle when sketching quadratics… now let’s combine our knowledge of the roots, and the y-intercept with the turning point so that we can sketch a quadratic showing it’s correct shape and labelling 4 points on the function. If you’ve forgotten about the roots and y-intercept you may want to quickly watch this video first... ( So that’s the axis of symmetry which we use to find the coordinates of the turning point. You are usually given the little formula, but check on your formula sheet or with your teacher as you may need to memorise. And then you substitute the x value into the quadratic to find the y-coordinate. SUBSCRIBE to the FuseSchool YouTube channel for many more educational videos. Our teachers and animators come together to make fun & easy-to-understand videos in Chemistry, Biology, Physics, Maths & ICT. VISIT us at www.fuseschool.org, where all of our videos are carefully organised into topics and specific orders, and to see what else we have on offer. Comment, like and share with other learners. You can both ask and answer questions, and teachers will get back to you. These videos can be used in a flipped classroom model or as a revision aid. Find all of our Chemistry videos here Find all of our Biology videos here Find all of our Maths videos here Twitter Access a deeper Learning Experience in the FuseSchool platform and app: www.fuseschool.org Follow us Friend us This Open Educational Resource is free of charge, under a Creative Commons License: Attribution-NonCommercial CC BY-NC ( View License Deed ). You are allowed to download the video for nonprofit, educational use. If you would like to modify the video, please contact us: info@fuseschool.org\n
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- 12th - Higher Ed
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![\"Quadratic](\"https://static.lp.lexp.cloud/images/attachment_defaults/resource/large/missing.png\" "\\"Quadratic")
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