Lesson 3.1 Extra Practice
STUDENT BOOK PAGES 140–147
1. State whether the parabola opens up or down.
a) f (x) ⫽ 4x 2
b) f (x) ⫽ ⫺3 (x ⫺ 6 ) (x ⫺ 8 )
c) f (x) ⫽ ⫺(x ⫹ 7 ) 2 ⫺ 9
d) f (x) ⫽ 9x 2 ⫹ 4x ⫺ 1
2. Given f (x) ⫽ ⫺2 (x ⫺ 7 )(x ⫹ 5 ) , state
a) the zeros
b) the direction of opening
c) the equation of the axis of symmetry
Copyright © 2008 by Thomson Nelson
3. Given f (x) ⫽ (x ⫺ 3 )( x ⫺ 4 ) , state
a) the zeros
b) the direction of opening
c) the equation of the axis of symmetry
4. Graph each function.
a) f (x ) ⫽ 2x 2 ⫺ 4
b) f (x) ⫽ (x ⫹ 1 ) 2 ⫺ 2
c) f (x) ⫽ 2 (x ⫹ 1 )(x ⫺ 2 )
1
d) f (x) ⫽ ⫺ x 2 ⫹ 3
2
5. Express each quadratic function in standard form.
State the y-intercept of each.
a) f (x) ⫽ ⫺(x ⫺ 6 )(x ⫹ 5 )
b) f (x) ⫽ ⫺4 (x ⫺ 2 ) 2
c) f (x) ⫽ 5 (x ⫹ 3 ) 2 ⫹ 2
d) f (x) ⫽ 7 (x ⫺ 1 )(x ⫺ 8 )
y
6.
5
4
3
2
1
–4 –3 –2 –1 0
–1
–2
–3
x
1
2 3 4
For the parabola above:
a) State the direction of opening.
b) Name the coordinates of the vertex.
c) List the values of the x-intercepts.
d) State the domain and range of the function.
e) Determine the algebraic model for this quadratic
function.
y
7.
6
5
4
3
2
1
–4 –3 –2 –1 0
–1
–2
x
1
2 3 4
Examine the parabola above.
a) State the direction of opening.
b) Find the coordinates of the vertex.
c) What is the equation of the axis of symmetry?
d) State the domain and range of the function.
8. Each pair of points (x, y) are the same distance from
the vertex of their parabola. Determine the equation
of the axis of symmetry of each parabola.
a) (5, 5), (⫺5, 5)
b) (4, 2), (⫺6, 2)
c) (1, ⫺9) , (8, ⫺9)
1
1
d) a⫺2, b , a3, b
4
4
9. The height of a balloon above the ground is
modelled by the quadratic function
h(t) ⫽ ⫺2t 2 ⫹ 18t, where h(t) is the height in
meters, t minutes after the balloon is launched.
a) Graph the quadratic function.
b) How long will the balloon be in the air? How do
you know?
c) How high will the balloon be after 3 minutes?
d) What is the maximum height that the balloon
will reach?
Lesson 3.1 Extra Practice
405