Parabola - Merit Mahobe. Basics first Movement in y direction.
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Transcript of Parabola - Merit Mahobe. Basics first Movement in y direction.
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Parabola - Merit
Mahobe
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Basics first
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Movement in y direction
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Movement in x direction
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Reflection in x-axis
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Stretch in y-direction e.g. height doubles
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Stretch in x-direction e.g. width halves
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Sketch
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Sketch
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Sketch
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Sketch
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Sketch
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Sketch
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Factored form of a quadratic
• Draw
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• Find the intercepts by putting x = 0 and y = 0
• Y-intercept is (0, -15)
• X-intercepts are (5, 0) and (-3, 0)
• The line of symmetry is half way between these points at x = 1 and y = -16
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• Find the intercepts by putting x = 0 and y = 0
• Y-intercept is (0, -15)
• X-intercepts are (5, 0) and (-3, 0)
• The line of symmetry is half way between these points at x = 1 and y = -16
![Page 18: Parabola - Merit Mahobe. Basics first Movement in y direction.](https://reader030.fdocuments.in/reader030/viewer/2022032709/56649ebf5503460f94bca4e6/html5/thumbnails/18.jpg)
Sketch these graphs
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• Note that this is just
• Moved down 3
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Sketch the following graphs with their axis of symmetry and give the coordinates of the vertex
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Vertex (3.5, -6.25)
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Vertex (-4, -36)
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Vertex (1, -36)
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Vertex (1.5, -2.25)
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A is (0, -6) or if the diagram is to scale (1, -4)
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B (-3, 0)
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C (2, 0)
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D (-0.5, 0)
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E (-0.5, -6.25)
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A stone is fired from a catapult. The height gained by the stone is given by the equation
• h= height of the stone• t = time in seconds• At what times is the stone at a height of 25
metres?
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Use the calculator to solve and round to appropriate level:
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What is the stone’s height after 2.5 seconds?
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Use the calculator to solve and round to appropriate level:
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Owen and Becks are playing football. Owen receives a pass and quickly kicks the ball towards Becks. The graph below shows the path of the ball
as it travels from Owen to Becks. The graph has the equation
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Find the value of the y-intercept and explain what this value represents.
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X = 0 y = 0.5 This means the ball’s initial height was 0.5 m
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Find the maximum height that the ball reaches.
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Halfway between 5 and -1 is 2. Substitute x = 2. the height is 0.9 metres above the ground.
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The graphs of y = -x and y = x(x + 2) are shown. Write down the co-ordinates of A and B.
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The graphs of y = -x and y = x(x + 2) are shown. Write down the co-ordinates of A and B.
A(-3, 3)B(-2, 0)
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Michael throws a cricket ball. The height of the ball follows the equation: h = 20x – 4x2 where h is the height in metres that the
ball reaches and x is the time in seconds that the ball is in the air.
Describe what happens to the ball: What is the greatest height? How long is it in the air?
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Michael throws a cricket ball. The height of the ball follows the equation: h = 20x – 4x2 where h is the height in metres that the
ball reaches and x is the time in seconds that the ball is in the air.
Maximum height is 25 metres and the ball is in the air for 5 seconds.
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When x = 2, y = 8, so the truck can travel through the tunnel.
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A theme park roller-coaster ride includes a parabolic shaped drop into a tunnel from a height of 45 metres. This drop can be modelled by
y = x2 – 14x +45. Draw the graph.
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Where does the bottom of the drop occur?
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The bottom of the drop is at 7 metres.
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How many metres does the roller-coaster drop from top to bottom?
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From 45 to -4. A height of 49 metres.
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Write x2 -14x + 45 in perfect square form.
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Write x2 -14x + 45 in perfect square form.
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Find the equation of the following parabolas.
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Don’t forget the stretch
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Gyn cannot reach the ball as he can only reach to a height of 2.7 m