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90148 Graphs 2006

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Question 1 Use the grids to draw the graphs of:

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y = 2x − 5

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x = 4

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y = (x − 2)(x + 4)

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Question 2 Parts of the Dare-devil and Easy-street ramps can be seen from the end of the spectator stand at a dirt cycle track. The graph below shows the height above ground level of the two ramps.

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What is the height of the Dare-devil ramp at the end of the spectator stand?

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0.5m

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What is the increase in height of the Easy-street ramp over the 15 m from the end of the spectator stand?

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0.5m for every 5 m 1.5m for 15 m

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At what distance, from the end of the spectator stand, are the two ramps the same height?

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5 m

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Question 3 Write the equations of the lines drawn on the grid below:

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Question 4 Use the grids to draw the graphs of:

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4y − 2x = 8

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y = 3 − 2x − x 2 = (1 − x)(3 + x)

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y = x 2 − 6x

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Question 5 Part of the dirt cycle track is shown on the graph below. The first section, AB, is a straight line and the second section, BCD, is part of a parabola.

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The equation of the second section, BCD, is It begins at B, a horizontal distance of 40 metres from the start.

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How high is the start of this second section, B, above ground- level?

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Substitute in x = 40 gives y = 4

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The point A is 6 metres above the ground. What is the gradient of the first section AB?

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How high above ground-level is the lowest point, C?

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1 metre

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In the graph below, the dotted line DEF shows the path of a rider performing a jump. The rider leaves the track at D, jumps to maximum height at E, and lands on a platform at F. This jump can also be modelled by a parabola. E is 8 metres above the ground and a horizontal distance of 60 metres from the start. B and D are both the same height above the ground. F is a horizontal distance of 72 metres from the start.

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Calculate the height of the platform at F.

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Point D (50, 4) lies on this parabola

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Modeling With Quadratic Functions Section 2.4 beginning on page 76.

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