Quadratic expression

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QUESTION
1. (10 marks) Identify the intervals of increase/decrease, the symmetry, and the domain
and range of each function.
a) f(x) = 3x
b) f(x) = x
2 + 2
c) f(x) = 2x − 1
2. (10 marks) Estimate the instantaneous rate of change for each function at each given
point. Identify any point that is a maximum/minimum value.
a) h(p) = 2p
2 + 3p; p = −1, −0.75 and 1
b) k(x) = −0.75x
2 + 1.5x + 13; x = −2, 4, and 1
3. (10 marks) Sketch the graph of f(x) = (x − 3)(x + 2)(x + 5) using the zeros and end
behaviours.
4. (10 marks) Solve the following inequality using graphing technology:
x
3 − 2x
2 + x − 3 ≥ 2x
3 + x
2 − x + 1
5. (10 marks) The population of locusts in a Prairie a town over the last 50 years is
modelled by the function
f(x) = 75x
x
2 + 3x + 2
The locusts population is given in hundreds of thousands. Describe the locust population
in the town over time, where x is time in years.
6. (10 marks) Select a strategy to solve each of the following.
Eton Academy 1 North York, Canada
MHF4U: Midterm Exam Revision – January 15, 2022
a) −x
x − 1
=
−3
x + 7
b) 2
x + 5
>
3x
x + 10
7. (10 marks) The following graphs (f(x) and g(x)) are a sine curve and a cosine curve,
determine the equations of the graphs

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