MPM2D Sample Exam Questions: Quadratic Relations

Overall Expectations:

• determine the basic properties of quadratic relations;

• relate transformations of the graph of y = x2 to the algebraic representationy = a(x – h)2+ k;

• solve quadratic equations and interpret the solutions with respect to the corresponding relations;

• solve problems involving quadratic relations.

1. Below is a graph of the parabola with equation . Graph the parabola with equation on the same grid. Clearly indicate 5 points on the graph.

2. Solve.

3. Rob was asked to determine the vertex of the parabola with equation . Using his algebra tiles, Rob came up with the correct representation below. State the vertex of the parabola. You may use any method.

Vertex: ______

4. A teacher asks his class to come up with a model for a quadratic relation that has a maximum of 8 and zeros of and 6. Below are three students’ models.

Ahmed’s Model / Bo’s Model / Cindy’s Model
x / y / /
-3 / -2
-2 / 0
-1 / 2
0 / 4
1 / 6
2 / 8
3 / 6
4 / 4
5 / 2
6 / 0
7 / -2

Give each student feedback by comparing their model to the quadratic relation described by the teacher.

5. Paula and Francine have each designed and tested a mini-rocket during their summer science camp at the Museum of Science and Technology. Paula’s rocket lands 20 metres from the launch point and achieves a maximum height of 60 metres. Francine’s rocket, launched from the same point, lands 40 metres away and also achieves a maximum height of 60 metres.

a) Whymight the flight paths be different? Explain your thinking. (Assume that they follow parabolic trajectories.)

b) The rockets are launched towards a 20 m tall observation building. If both rockets clear the observation building, determine what you can about the width of the building? Justify your answer.

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