Parabola - Merit Mahobe

Basics first

Movement in y direction

Movement in x direction

Reflection in x-axis

Stretch in y-direction e.g. height doubles

Stretch in x-direction e.g. width halves

Sketch

Factored form of a quadratic Draw

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

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

Sketch these graphs

Note that this is just Moved down 3

Sketch the following graphs with their axis of symmetry and give the coordinates of the vertex

Vertex (3.5, -6.25)

Vertex (-4, -36)

Vertex (1, -36)

Vertex (1.5, -2.25)

A is (0, -6) or if the diagram is to scale (1, -4)

B (-3, 0)

C (2, 0)

D (-0.5, 0)

E (-0.5, -6.25)

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?

Use the calculator to solve and round to appropriate level:

What is the stone’s height after 2.5 seconds?

Use the calculator to solve and round to appropriate level:

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

Find the value of the y-intercept and explain what this value represents.

X = 0 y = 0.5 This means the ball’s initial height was 0.5 m

Find the maximum height that the ball reaches.

Halfway between 5 and -1 is 2. Substitute x = 2. the height is 0.9 metres above the ground.

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)

Michael throws a cricket ball. The height of the ball follows the equation: h = 20x – 4x 2 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?

Michael throws a cricket ball. The height of the ball follows the equation: h = 20x – 4x 2 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.

When x = 2, y = 8, so the truck can travel through the tunnel.

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 = x 2 – 14x +45. Draw the graph.

Where does the bottom of the drop occur?

The bottom of the drop is at 7 metres.

How many metres does the roller-coaster drop from top to bottom?

From 45 to -4. A height of 49 metres.

Write x 2 -14x + 45 in perfect square form.

Find the equation of the following parabolas.

Don’t forget the stretch

Gyn cannot reach the ball as he can only reach to a height of 2.7 m