Lesson 3.2 Extra Practice
STUDENT BOOK PAGES 148–154
1. Which of the following quadratic functions will
have a maximum or minimum value? Explain how
you know.
a) f (x) ⫽ 3x 2
b) f (x) ⫽ ⫺4 (x ⫺ 1 )(x ⫺ 5 )
c) f (x) ⫽ ⫺(x ⫹ 2 ) 2 ⫺ 9
d) f (x) ⫽ 8x 2 ⫹ 5x ⫺ 2
2. Determine the maximum or minimum value.
Use at least two different methods.
a) f (x) ⫽ 3x 2
b) f (x) ⫽ 3x 2 ⫺ 12x ⫹ 1
c) f (x) ⫽ (x ⫹ 6 ) 2 ⫺ 5
d) f (x) ⫽ ⫺9 (x ⫹ 2 )(x ⫺ 4 )
e) f (x) ⫽ (x ⫺ 4 )(x ⫺ 4 )
f ) f (x ) ⫽ ⫺2x 2 ⫺ 8x ⫹ 6
Copyright © 2008 by Thomson Nelson
3. Each function is the demand function of some
item, where x is the number of items sold, in
thousands. Determine
i) the revenue function
ii) the maximum revenue in thousands of dollars
a) p (x) ⫽ ⫺2x ⫹ 12
b) p (x) ⫽ ⫺4x ⫹ 16
c) p(x) ⫽ ⫺2x ⫺ 8
d) p (x) ⫽ ⫺4.5x ⫹ 1.7
4. Use a graphing calculator to determine the
maximum or minimum value. Round to two
decimal places where necessary.
a) f (x) ⫽ 8x 2 ⫹ 5.1x ⫺ 3.5
b) f (x) ⫽ ⫺1.2x 2 ⫹ 2.4x
c) f (x) ⫽ 3.6x 2 ⫹ 7.2x ⫹ 5.4
d) f (x) ⫽ 4x 2 ⫺ 5.2x
6. The profit P(x) of a cosmetics company,
in thousands of dollars, is given by
P(x) ⫽ ⫺6x 2 ⫹ 240x ⫺ 1500. where
x is the amount spent on advertising, in
thousands of dollars.
a) Determine the maximum profit the company can
make.
b) Determine the amount spent on advertising that
will result in the maximum profit.
c) What amount must be spent on advertising to
obtain a profit of at least $500 000?
7. The cost function in a bicycle manufacturing plant
is C (x) ⫽ 0.24x 2 ⫺ 0.5x ⫹ 2, where C(x) is the
cost per hour in millions of dollars and x is the
number of items produced per hours in thousands.
Determine the minimum production cost.
8. The height of a ball thrown vertically upward from
a rooftop is modelled by h(t) ⫽ ⫺4t 2 ⫹ 32t ⫹ 15,
where h(t) is the ball’s height above the ground, in
metres, at time t seconds after the throw.
a) Determine the maximum height of the ball.
b) How long does it take for the ball to reach its
maximum height?
c) How high is the rooftop?
9. Compare the methods for finding the minimum
value of the quadratic function
f (x ) ⫽ 7x 2 ⫺ 3x ⫹ 1. Which method would you
choose for this particular function? Give a reason
for your answer.
5. For each pair of revenue and cost functions,
determine
i) the profit function
ii) the value of x that maximizes profit
a) R(x) ⫽ ⫺x 2 ⫹ 19x, C (x) ⫽ 3x ⫹ 5
b) R(x) ⫽ ⫺4x 2 ⫹ 28x, C(x) ⫽ 4x ⫹ 1
c) R (x) ⫽ ⫺2x 2 ⫹ 20x, C (x) ⫽ 16x ⫹ 11
d) R (x) ⫽ ⫺3x 2 ⫹ 26x, C(x) ⫽ 2x ⫹ 24
Lesson 3.2 Extra Practice
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