Lesson 3.8 Extra Practice
STUDENT BOOK PAGES 194–199
1. Find the point(s) of intersection by graphing.
a) f (x ) ⫽ x 2, g(x) ⫽ x ⫹ 2
1
b) f (x) ⫽ ⫺7x 2, g(x) ⫽ x ⫹ 6
2
c) f (x) ⫽ ⫺3x 2 ⫹ 4, g(x) ⫽ x ⫺ 4
d) f (x) ⫽ (x ⫺ 3 ) 2 ⫹ 2, g(x) ⫽ ⫺5x ⫺ 5
2. Determine the point(s) of intersection algebraically.
a) f (x) ⫽ ⫺2x 2 ⫹ 1, g(x) ⫽ ⫺3x ⫺ 2
b) f (x) ⫽ 5x 2 ⫹ 4, g(x) ⫽ 2x ⫹ 6
c) f (x) ⫽ ⫺4x 2 ⫺ 1, g(x) ⫽ ⫺7x ⫺ 1
d) f (x) ⫽ ⫺2x 2 ⫺ 5x ⫹ 3, g(x) ⫽ ⫺9x ⫹ 4
3. Determine the number of points of intersection of
f (x) ⫽ 3x 2 ⫺ 5x ⫹ 2 and g(x) ⫽ 7x ⫹ 1
without solving.
4. Determine the point(s) of intersection of each pair
of functions.
a) f (x) ⫽ ⫺8x 2 ⫹ 9, g(x) ⫽ ⫺3x ⫺ 9
b) f (x) ⫽ ⫺x 2 ⫹ 5, g(x ) ⫽ 3x ⫹ 2
c) f (x) ⫽ ⫺6x 2 ⫺ 3, g(x) ⫽ ⫺2x ⫺ 4
d) f (x) ⫽ x 2 ⫺ 4x ⫹ 1, g(x) ⫽ ⫺7x ⫹ 5
Copyright © 2008 by Thomson Nelson
5. An integer is one more than another integer. Twice
the larger integer is three more than the square of
the smaller integer. Find the two integers.
6. The revenue function for a production by a theatre
group is R (t) ⫽ ⫺75t2 ⫹ 500t, where t is the
ticket price in dollars. The cost function for the
production is C (t ) ⫽ 400 ⫺ 50t. Determine the
ticket price that will allow the production to break
even.
7. a) Copy the graph of f (x) ⫽ (x ⫺ 3) 2 ⫺ 4. Then
draw lines with slope ⫺5 that intersect the
parabola at (i) one point, (ii) two points, and
(iii) no points.
b) Write the equations of the lines from part (a).
c) How are all of the lines with slope ⫺5 that do
not intersect the parabola related?
y
8
6
4
2
–6 –4 –2 0
–2
–4
–6
x
2 4 6
8. Determine the value of k such that g(x) ⫽ 4x ⫹ k
intersects the quadratic function
f (x) ⫽ 3x 2 ⫺ 5x ⫹ 2 at exactly one point.
9. A daredevil jumps off the CN Tower and falls freely
for several seconds before releasing his parachute.
His height, h(t) , in metres, t seconds after jumping
can be modelled by h1 (t) ⫽ ⫺8.1t 2 ⫹ t ⫹ 320
before he released his parachute; and
h1 (t) ⫽ ⫺8t 2 ⫹ 145 after he released his
parachute. How long after jumping did the
daredevil release his parachute?
10. A punter kicks a football. Its height, h(t) , in
metres, t seconds after the kick is given by the
equation h(t) ⫽ ⫺4.5t 2 ⫹ 19.25t ⫹ 0.6. The
height of an approaching blocker’s hands is
modelled by the equation g(t) ⫽ ⫺1.32t ⫹ 3.75,
using the same t. Can the blocker knock down the
punt? If so, at what point will it happen?
11. Determine the value(s) of k such that the linear
function g(x) ⫽ 6x ⫹ k does not intersect the
parabola f (x) ⫽ ⫺5x 2 ⫺ x ⫹ 6.
Lesson 3.8 Extra Practice
421