CURVE GRAPHS .

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Presentation transcript:

CURVE GRAPHS

y = ax2 Single Focus Path of a Moving Object Receiver Transmitter Radio Telescope Torch Reflector Satellite Dish Receiver Transmitter y = ax2 Path of a Moving Object Single Focus A Parabolic device has a single focus. This enables radiation to be received and amplified or transmitted and amplified.

1 2 3 4 5 6 7 8 9 10 -9 -8 -7 -6 -5 -4 -3 -2 -1 -10 x y y = x2 y = x2 - 5 y = x2 + 1

1 2 3 4 5 6 7 8 9 10 -9 -8 -7 -6 -5 -4 -3 -2 -1 -10 x y 11 12 13 14 15 16 17 18 19 20 y = x2 y = 2x2 y = 3x2 As the coefficient of x2 becomes larger, the curve becomes compressed in the x direction towards the y axis .

1 2 3 4 5 6 7 8 9 10 -9 -8 -7 -6 -5 -4 -3 -2 -1 -10 x y y = x2 y = ½x2 y = ¼x2 As the the coefficient of x becomes smaller, the curve opens up. It is stretched in the x direction away from the y axis.

Equation of Line of symmetry is x = 1 1 2 3 4 -1 -2 5 6 7 8 -3 -4 -5 -6 -7 -8 y -9 x LoS Drawing quadratic graphs of the form y = ax2 + bx + c Example 1. Equation of Line of symmetry is x = 1 y = x2 - 2x - 8 x -3 -2 -1 1 2 3 4 5 x2 -2x -8 y 9 4 1 1 4 9 16 25 6 4 2 -2 -4 -6 -8 -10 -8 7 -5 -8 -9 -8 -5 7 Minimum point at (1, -9)

Equation of Line of Symmetry is x = - 2½ Example 2. Drawing quadratic graphs of the form y = ax2 + bx + c 1 2 3 4 -1 -2 -3 -4 -5 5 6 7 8 -6 -7 -8 x y LoS y = x2 + 5x + 2 y 2 5x x2 1 -1 -2 -3 -4 -5 -6 x 36 25 16 9 4 1 1 -30 -25 -20 -15 -10 -5 5 2 8 2 -2 -4 -4 -2 2 8 Minimum point at (-2½, -4¼) approximately Equation of Line of Symmetry is x = - 2½

A negative x2 term inverts the curve. x y y = -x2 + 2x + 8 y = -x2 - 5x - 2 A negative x2 term inverts the curve.

y Example question x  (a) Draw the graph of y = x2 - 4x - 5 -3 1 2 3 4 -1 -2 5 6 7 8 -4 -5 -6 -7 -8 -9 x Example question (a) Draw the graph of y = x2 - 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