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Path of a Moving Object Radio Telescope Torch Reflector Satellite Dish Receiver Transmitter y = ax 2 A Parabolic device has a single focus. This enables radiation to be received and amplified or transmitted and amplified. Single Focus

y = x y = x y = x x y

y = 2x 2 y = 3x 2 y = x 2 As the coefficient of x 2 becomes larger, the curve becomes compressed in the x direction towards the y axis x y

y = ½x 2 y = ¼x 2 As the the coefficient of x becomes smaller, the curve opens up. It is stretched in the x direction away from the y axis. y = x x y

y x y = x 2 - 2x - 8 x x2x2 -2x -8 y LoS Equation of Line of symmetry is x = 1 Drawing quadratic graphs of the form y = ax 2 + bx + c Example 1. Minimum point at (1, -9)

Example 2. Drawing quadratic graphs of the form y = ax 2 + bx + c x y y = x 2 + 5x + 2 y 2 5x x2x x Equation of Line of Symmetry is x = - 2½ Minimum point at (-2½, -4¼) approximately LoS

0 x y y = -x 2 + 2x x y y = -x 2 - 5x - 2 A negative x 2 term inverts the curve.

y x 6 Example question (a) Draw the graph of y = x 2 - 4x - 5 (b) Write down the co-ordinates of the minimum point. (c) Write down the equation of the line of symmetry. (d) Find the value of y when x = 2½. (e) Find the values of x when y = -8. (a) (b) (c) (d) (e)  (2, -9) x = 2 y = -8.7 (approx) x = 1 and 3

1 2 3 x x x y y y

x y y = x 2 + 5x + 2 y 2 5x x2x x Example 2