Grade 11 Mathematics
Unit 7.1: Quadratic Functions
Exercise 7.1
1. Determine the x and y coordinates of the turning points of the following functions:
a) 𝑦(𝑥) = 9(𝑥 − 1)2 − 4
b) 𝑦(𝑥) = 4𝑥 2 − 1
c) ℎ(𝑥) = −(𝑥 + 2)2 + 1
d) ℎ(𝑥) = −(𝑥 − 4)2 + 4
e) ℎ(𝑥) = −9(𝑥 + 1)2 + 16
2. Determine the turning point for each of the following functions:
a) 𝑦(𝑥) = 9(𝑥 − 1)2 − 4
b) 𝑦(𝑥) = 4𝑥 2 − 1
c) ℎ(𝑥) = −(𝑥 + 2)2 + 1
d) ℎ(𝑥) = −(𝑥 − 4)2 + 4
e) ℎ(𝑥) = −9(𝑥 + 1)2 + 16
3. Determine the axis of symmetry of each of the following functions:
a) 𝑦(𝑥) = 9(𝑥 − 1)2 − 4
b) 𝑦(𝑥) = 4𝑥 2 − 1
c) ℎ(𝑥) = −(𝑥 + 2)2 + 1
d) ℎ(𝑥) = −(𝑥 − 4)2 + 4
e) ℎ(𝑥) = −9(𝑥 + 1)2 + 16
4. Consider the quadratic function below.
The quadratic coefficient is 𝑎 = 1. Determine the equation of the function.
5. The diagram below shows three parabolas. They were named A, B, and C.
Which of the following graphs corresponds to the function
𝑓(𝑥) = (𝑥 − 5)2 − 2?
6. Consider the quadratic function below. The quadratic coefficient is
𝑎 = 1. Determine the equation of the function.
7. The diagram below shows three parabolas. They were named A, B, and C.
Which of the following graphs corresponds to the function
1
𝑓(𝑥) = − 2 (𝑥 − 3)2 + 1?
8. Sketch the following functions. Write down the turning point of each function as
well as whether it is a maximum or minimum.
a) 𝑦 = − 𝑥² + 2𝑥 − 3
b) 𝑦 = 𝑥² − 3𝑥 − 4
c) 𝑦 = 𝑥² − 8𝑥 + 15
d) 𝑦 = − 2𝑥² + 7𝑥 − 9
e) 𝑦 = 𝑥² + 8𝑥 + 9
f) 𝑦 = 2𝑥² + 5𝑥 − 6
g) 𝑦 = − 3𝑥² + 10𝑥 − 9
h) 𝑦 = 5𝑥² − 9𝑥 + 4
1
i) 𝑦 = − 2 𝑥 2 − 3𝑥 − 2
1
1
j) 𝑦 = 4 𝑥 2 + 2 𝑥 + 1
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