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2. 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

3. y = x 2 - 5 y = x 2 + 1 y = x 2 0 1234567 8 910 -9-8 -7 -6 -5 -4-3-2 -10 x y 1 2 3 4 5 6 7 8 9 10 -2 -3 -4 -5 -6 -7 -8 -9 -10

4. 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. 0 1234567 8 910 -9-8 -7 -6 -5 -4-3-2 -10 x y 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

5. 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 2 0 1234567 8 910 -9-8 -7 -6 -5 -4-3-2 -10 x y 1 2 3 4 5 6 7 8 9 10 -2 -3 -4 -5 -6 -7 -8 -9 -10

6. 012 3 4 -2 1 2 3 4 5 6 7 8 -2 -3 -4 -5 -6 -7 -8 5 y -3 -9 x y = x 2 - 2x - 8 x -3-2-1 012345 x2x2 -2x -8 y 94 101 4 9 1625 6 4 20-2 -4 -6-8 -10 -8 70-5-8 -9-8-50 7 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)

7. Example 2. Drawing quadratic graphs of the form y = ax 2 + bx + c 012 3 4 -2 -3 -4 -5 1 2 3 4 5 6 7 8 -2 -3 -4 -5 -6 -7 -8 -6 x y y = x 2 + 5x + 2 y 2 5x x2x2 10-2-3-4-5-6x 36 25 169 4 1 0 1 -30-25 -20-15-10-5 05 222222 2 2 82 -2 -4 -22 8 Equation of Line of Symmetry is x = - 2½ Minimum point at (-2½, -4¼) approximately LoS

8. 0 x y y = -x 2 + 2x + 8 0 x y y = -x 2 - 5x - 2 A negative x 2 term inverts the curve.

9. y -3 012 3 4 -2 1 2 3 4 5 6 7 8 -2 -3 -4 -5 -6 -7 -8 5 -9 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

10. 1 2 3 x x x y y y

12. 012 3 4 -2 -3 -4 -5 1 2 3 4 5 6 7 8 -2 -3 -4 -5 -6 -7 -8 -6 x y y = x 2 + 5x + 2 y 2 5x x2x2 10-2-3-4-5-6x Example 2