1. Learning Objectives To recognise and plot quadratic graphs
Curved Line Graphs
Learning Objectives
To recognise and plot quadratic graphs

2. Ballistics y = -5x2 + ux y = -5x2 + 200x
When an object is thrown into the air, its distance above the ground is given by this equation:
y = -5x2 + ux
(y is the distance, x is the time, u is the speed)
Plot the graph of a bullet shot at 200m/s:
y = -5x x
What is the maximum height reached?
How far above the ground is the bullet after 10s?

3. Maximising Range
Initial Speed at 45° to the horizontal
Parabolic path

5. How to sketch a quadratic
Eg. y = x2 + 3x + 2
Find the point where it crosses the y-axis (ie where x = 0)
Find the point(s) – if any – where it crosses the x-axis (ie where y = 0)
Find the maximum or minimum point (if positive x2 min, if negative, max)
Substitute x = 0 into equation
y = x2 + 3x + 2
y = (0)2 + 3(0) + 2 = 2 2
(x + 1)(x + 2) = 0
x = -1, x = -2 -2 -1
Factorise, complete the square or use the formula
(-1.5,-0.25)
y = (x + 1.5)2 –
y = (x + 1.5)2 – 0.25
Min: y = at x = -1.5
Complete the square

6. Sketch the following graphs.
Remember to give co-ordinates of any points where the graph crosses the axes and any minimum or maximum points.

9. Focus