Lesson 3.5 Extra Practice
STUDENT BOOK PAGES 172–178
1. Determine the roots of each equation by factoring.
a) x 2 ⫹ 5x ⫹ 6
b) x 2 ⫺ x ⫺ 12
c) x 2 ⫺ 12x ⫹ 36
d) 25x 2 ⫺ 16
e) 2x 2 ⫺ 5x ⫺ 3
f ) x 2 ⫹ x ⫺ 30
2. Use the quadratic formula to determine each of the
roots to two decimal places.
a) 2x 2 ⫹ 3x ⫹ 1
b) x 2 ⫺ 6x ⫺ 2
c) 4x 2 ⫺ 9x ⫺ 12
d) 2x 2 ⫺ 9
e) x 2 ⫺ 7x ⫺ 2
f ) 5x 2 ⫹ 2x ⫺ 3
Copyright © 2008 by Thomson Nelson
3. Use a graphing calculator to solve each equation.
a) ⫺x 2 ⫺ 9x ⫺ 4 ⫽ 0
b) x 2 ⫹ 5x ⫺ 6 ⫽ 0
c) 2x 2 ⫺ 9x ⫹ 2 ⫽ 0
d) 3x 2 ⫺ 8x ⫹ 1 ⫽ 0
4. i) For each equation, decide on a strategy to solve it
and explain why you chose that strategy.
ii) Use your strategy to solve the equation. When
appropriate, leave your answer in simplest radical
form.
a) x 2 ⫹ 4x ⫽ ⫺x 2 ⫹ 5x
b) x 2 ⫹ 3x ⫽ ⫺10x 2 ⫺ 3x
c) x 2 ⫺ 5x ⫹ 6 ⫽ 0
d) x 2 ⫹ 9x ⫺ 1 ⫽ 0
e) (x ⫹ 3 ) 2 ⫽ ⫺3x
f ) (x ⫹ 3 ) (x ⫺ 3 ) ⫽ 3x ⫹ 2
6. The flight of a ball hit from a tee that is 1.5 m tall
can be modelled by the function
h(t) ⫽ ⫺5.2t ⫹ 3t ⫹ 0.5, where h(t) is the
height in metres at time t seconds. How long will it
take for the ball to hit the ground?
7. The population of a region in thousands can be
modelled by the function P(t ) ⫽ 0.2t 2 ⫹ 6t ⫹ 30
where P(t) is the population in thousands and t is
the time in years since the year 1970.
a) What was the population in 1970?
b) What will be the population in 2015?
c) In what year will the population be at least
250 000? Explain your answer.
8. A rectangle has an area of 400 m2. One side is 5 m
longer than the other. What are the dimensions of
the rectangle?
9. The sum of the squares of two consecutive integers
is 145. What could the integers be? List all
possibilities.
10. A right triangle has a height 9 cm more than twice
the length of the base. If the area of the triangle is
55.93 cm2, what are the dimensions of the triangle?
11. A small flare is launched off the deck of a ship. The
height of the flare above the water is given by the
function h(t) ⫽ ⫺5.2t 2 ⫹ 84t ⫹ 16 where h(t ) is
measured in metres and t is time in seconds.
a) When will the flare’s height be 150 m?
b) How long will the flare’s height be above 150 m?
5. Determine the break-even quantities for each profit
function, where x is the number sold, in thousands.
a) P(x) ⫽ ⫺3x 2 ⫹ 25x ⫹ 5
b) P(x) ⫽ ⫺x 2 ⫹ 5x ⫹ 9
c) P(x) ⫽ ⫺6x 2 ⫹ 4x ⫹ 8
d) P(x) ⫽ ⫺x 2 ⫹ 9x ⫹ 3
e) P(x ) ⫽ ⫺.75x 2 ⫹ .5x ⫹ .25
f ) P(x) ⫽ 1.5x 2 ⫺ 6x ⫺ 14
Lesson 3.5 Extra Practice
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