Expand and simply the following expressions. (4 marks).
Factor fully. (4 marks)
The expression 
Solve the following quadratic equations. (5 marks).
Either,
Or,
Therefore,
Describe the transformations in each of the following quadratic equations as they compare to the standard parabola 
This is graphically shown in Figure 1.
Figure 1: Transformation
The parabola will shift right by 4 units. It will be vertically compressed, and be reflected along the x-axis.
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The parabola will shift horizontally by 2 units, vertically by 2 units, and will be stretched.
Complete the following tables of values and graph each relation. (2 x 6 marks).
| x | y | 1 st diff. | 2 nd diff. |
-3 | -9 | ||
-2 | -7 | 2 | |
-1 | -5 | 2 | 0 |
0 | -3 | 2 | 0 |
1 | -1 | 2 | 0 |
2 | 1 | 2 | 0 |
3 | 3 | 2 | 0 |
| x | y | 1 st diff. | 2 nd diff. |
-3 | -8 | ||
-2 | -9 | -1 | |
-1 | -8 | 1 | 2 |
0 | -5 | 3 | 2 |
1 | 0 | 5 | 2 |
2 | 7 | 7 | 2 |
3 | 16 | 9 | 2 |
What do the first and second difference tells us about these equation? Be specific in your expiations.
The first and second difference tell if an equation is linear or quadratic. If the first and second differences are all equal, then the equation is linear. If the first difference are not equal but the second difference are equation, then the equation is quadratic.
Complete the following table for each parabola. (2 x 10 marks).
Parabola A | Parabola B | ||
Vertex | (-4,4) | Vertex | (1,-8) |
Axis of Symmetry | Axis of Symmetry | ||
Direction of Opening | Down | Direction of Opening | Up |
Min/Max | Min/Max | ||
Optimum Value | 4 | Optimum Value | -8 |
Zeros | Zeros | ||
y-intercept | y-intercept | ||
Step Pattern | -1, -3, -5 | Step Pattern | +2, +6, +12 |
Equation | Equation |
Equation of a parabola A:
Equation of Parabola B:
Complete the following table. (8 marks).
Equation | Vertex | Opens Up/Down | Step Pattern | Axis of Symmetry | Max or Min Value | |
a) | (0,0) | Down | -119, -153, -113 | |||
b) | (1,3) | Up | +42, +38, +34 | |||
c) | (5,-4) | Down | -3, -9, -15 |
a)
b)
c)
Graph and label each parabola on the grid below. [6 marks).
| x | y |
-10 | 1697 |
-9 | 1303 |
-8 | 975 |
-7 | 707 |
-6 | 493 |
-5 | 327 |
-4 | 203 |
-3 | 115 |
-2 | 57 |
-1 | 23 |
0 | 7 |
1 | 3 |
2 | 5 |
3 | 7 |
4 | 3 |
5 | -13 |
6 | -47 |
7 | -105 |
8 | -193 |
9 | -317 |
10 | -483 |
-10 | 63 |
-9 | 41 |
-8 | 23 |
-7 | 9 |
-6 | -1 |
-5 | -7 |
-4 | -9 |
-3 | -7 |
-2 | -1 |
-1 | 9 |
0 | 23 |
1 | 41 |
2 | 63 |
3 | 89 |
4 | 119 |
5 | 153 |
6 | 191 |
7 | 233 |
8 | 279 |
9 | 329 |
10 | 383 |
Match each parabola with the diagram below. Put the correct letter of parabola next to the corresponding equation. (4 marks).
C | D | |||
A | B | |||
Let’s us first determine the y-intercepts of the equations.
From the graphs, the parabola with a 
is parabola C
From the graphs, the parabola with a 
is parabola D
From the graphs, the parabola with a 
is parabola A
From the graphs, the parabola with a 
is parabola B
Cassandra drops a rock off of a bridge into the water below. The path of the rock of the can be modelled by the equation 
, where h is the height in feet and it is the time in seconds.
Draw a labelled sketch of this scenario. (1 mark)
How high is the bridge from the surface of the water? (2 marks)
At the time of release, 
Therefore,
What was the height of the rock after 3 seconds? (2 marks)
When will the rock hit the water’s surface?
In this case,
Therefore,
