Quadratic graphs.

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Presentation transcript:

Quadratic graphs

1 a Draw the graph of y = 2x2 – 3x – 2 in the range Put the results into a table and then draw the graph.

x 2 -1 1 3 4 y 12 -2 -3 7 18 1 4 3 -2 -1 5 10 15 2 y x 20 -5 x x x x x x x

y x b Use the graph to estimate the values of x when y = 9. and 1 4 3 1 4 3 -2 -1 5 10 15 2 y x 20 -5 x x x x x -1.7 3.2 x x

y x c By drawing a tangent to the graph estimate the gradient of the graph when x = 3. Gradient 1 4 3 -2 -1 5 10 15 2 y x 20 -5 x x x 18 x x x x 2

2 a Draw the graph of y = 9 + 3x - 3x2 in the range Put the results into a table and then draw the graph.

x 2 -1 1 3 y -9 9 y 15 10 x x 5 x x x -2 -1 1 2 3 -5 x x -10

y x b Use the graph to estimate the values of x when y = -4. and 1 3 1 3 -2 -1 5 10 15 2 x -10 -5 -1.6 2.6

y x c By drawing a tangent to the graph estimate the gradient of the graph when x = 1. Gradient y 1 3 -2 -1 5 10 15 2 x -10 -5 12 4