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Curved Line Graphs. Learning Objectives To recognise and plot quadratic graphs. Ballistics. When an object is thrown into the air, its distance above the ground is given by this equation: y = -5 x 2 + u x ( y is the distance, x is the time, u is the speed).
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Curved Line Graphs Learning Objectives To recognise and plot quadratic graphs
Ballistics • When an object is thrown into the air, its distance above the ground is given by this equation: y = -5x2 + ux (y is the distance, x is the time, u is the speed) Plot the graph of a bullet shot at 200m/s: y = -5x2 + 200x What is the maximum height reached? How far above the ground is the bullet after 10s?
Maximising Range Initial Speed at 45° to the horizontal Parabolic path
How to sketch a quadratic Eg. y = x2 + 3x + 2 • Find the point where it crosses the y-axis (ie where x = 0) • Find the point(s) – if any – where it crosses the x-axis (ie where y = 0) • Find the maximum or minimum point (if positive x2 min, if negative, max) Substitute x = 0 into equation y = x2 + 3x + 2 y = (0)2 + 3(0) + 2 = 2 2 (x + 1)(x + 2) = 0 x = -1, x = -2 -2 -1 Factorise, complete the square or use the formula (-1.5,-0.25) y = (x + 1.5)2 – 2.25 + 2 y = (x + 1.5)2 – 0.25 Min: y = -0.25 at x = -1.5 Complete the square
Sketch the following graphs. Remember to give co-ordinates of any points where the graph crosses the axes and any minimum or maximum points.
