Quadratic Relations PRACTICE Test	Know	App	Think	Comm Level

Knowledge and Understanding

1. Complete theanalysis for the following parabola. [6 marks]

Draw theaxis of symmetry and state its equation.
Draw and state thezeroes (x-intercepts).
Draw and state they-intercept.
State thedirection of opening of the parabola.
Draw and state thevertex as an (x, y) point.

1. a) Complete the table of values and graph the relation fory = x² - 4x using x valuesfrom -1 to 5. [9 marks]

x	y = x2 - 4x	(x, y)
-1
0
1
2
3
4
5

b) Complete the following analysis for your parabola above (y = x² - 4x). [6 marks]

Draw theaxis of symmetry and state its equation.
Draw and state thezeroes (x-intercepts).
Draw and state they-intercept.
State thedirection of opening of the parabola.
Draw and state thevertex as an (x, y) point.

1. a) Graphy = x² - 8x + 7 using thestyv speed graphing method. [8 marks]

b) Complete the following analysis for your parabola above (y = x² - 8x + 7). [6 marks]

Draw theaxis of symmetry and state its equation.
Draw and state thezeroes (x-intercepts).
Draw and state they-intercept.
State thedirection of opening of the parabola.
Draw and state thevertex as an (x, y) point.

1. In class we learned aboutthree ways to tell that a relation is quadratic. Describeanytwo of the three ways. [2 marks]

Application

1. A rock is thrown off a cliff into the water below according toy =-2x² + 8x + 10, wherey represents the height of the cliff, in metres, andx represents the time in seconds.

1. Complete the table of values using x valuesfrom -1 to 4 [10 marks]

x	y = -2x2 + 8x + 10	1st Difference	2nd Difference	(x, y)

1. Graph the relation. [2 marks]

1. Using your graph and table of values, answer each of the following questions. [6 marks]
   1. How high is the cliff? __________
   2. How high is the rock after 1.5 seconds? __________
   3. How long does it take the rock to hit the water? __________
   4. When is the rock at 14 m above the water? __________
   5. What is the maximum height reached by the rock? __________
   6. When does the rock reach its maximum height? __________

Thinking

1. A telephone cable is suspended between two poles. The height of the cable above the ground can be described by the equationy = 0.05x² - 1.35x + 15, wherey represents the height of the cable above the ground in metres, andx represents the distance of the cable from the first pole.

1. Complete the following chard and graph the relation. [8 marks]

Distance from the first pole, x (m)	Height of cable above ground, y (m)	1st Difference	2nd Difference
0	15
3	11.4
6	8.7
9	6.9
12	6
15	6
18	6.9
21	8.7
24	11.4
27	15

1. Graph the relation. [2 marks]

1. Is the relation linear or quadratic? Explain your reasoning based on thetableand graph. [2 marks]
2. How close to the ground does the cable sag and how far from the first pole does this occur? [2 marks]
3. How far from the ground is the cable when it is 20 m from the first pole? [1 mark]