Lesson 3.6 Extra Practice
STUDENT BOOK PAGES 179–186
1. Determine the vertex and the direction of opening
for each quadratic function. Then state the number
of zeros.
a) f (x) ⫽ 4x 2 ⫺ 6
b) f (x) ⫽ ⫺3x 2 ⫺ 9
c) f (x) ⫽ 5x 2 ⫹ 1
d) f (x) ⫽ 2 (x ⫺ 8 ) 2
e) f (x) ⫽ ⫺2 (x ⫺ 3 ) 2
f ) f (x) ⫽ 4 (x ⫺ 1 ) 2 ⫺ 2
2. Factor each quadratic function to determine the
number of zeros.
a) 2x 2 ⫹ 3x ⫹ 1
b) 4x 2 ⫺ 24x ⫺ 36
c) 2x 2 ⫺ 5x ⫺ 7
d) 3x 2 ⫹ 24x ⫹ 16
e) ⫺x 2 ⫹ 28x ⫺ 196
f ) x 2 ⫺ 25
Copyright © 2008 by Thomson Nelson
3. Calculate the value of b2 ⫺ 4ac to determine the
number of zeros.
a) 7x 2 ⫹ 3x ⫹ 1
b) ⫺x 2 ⫺ 2x ⫺ 5
c) 10x 2 ⫺ 22x ⫺ 2
d) 5x 2 ⫺ 5
e) 8x 2 ⫺ 4x ⫺ 9
f ) 5x 2 ⫹ 20x ⫹ 25
4. For each profit function, determine whether the
company can break even. If the company can break
even, determine in how many ways it can do so.
a) P(x) ⫽ ⫺4.2x 2 ⫹ 18.12x ⫺ 10.8
b) P(x) ⫽ ⫺5x 2 ⫹ 19x ⫺ 9
c) P(x) ⫽ ⫺5.1x 2 ⫹ 9x ⫺ 4
d) P(x) ⫽ ⫺3x 2 ⫹ 2.1x ⫺ 1.2
e) P(x ) ⫽ ⫺6.4x 2 ⫹ 3.7x ⫺ 4.8
f ) P(x) ⫽ ⫺x 2 ⫹ 1.5x ⫺ 3.6
7. For what values of k will the function
f (x) ⫽ 5x 2 ⫹ 6x ⫹ k have no zeros? one zero?
two zeros?
8. The graph of the function
f (x) ⫽ x 2 ⫺ kx ⫹ k ⫹ 5 touches the x-axis at one
point. What are the possible values of k?
9. The demand function for a new product is
p (x) ⫽ 5x ⫹ 38.2, where x is the quantity sold in
thousands and p is the price in dollars. The
company that manufactures the product is planning
to buy a new machine for the plant.
There are three different types of machine. The cost
function for each machine is shown.
Machine A: C (x) ⫽ 5.2x ⫹ 61.32
Machine B: C (x) ⫽ 21.4x ⫹ 23.5
Machine C: C (x) ⫽ 9.1x ⫹ 45.6
Investigate the break-even quantities for each
machine. Which machine would you recommend
to the company?
10. Determine the number of zeros of the function
f (x) ⫽ 5 ⫺ (x ⫺ 6) (4x ⫹ 5 ) without solving
the related quadratic equation or graphing. Explain
your thinking.
11. Write the equation of a quadratic function that
meets each of the given conditions.
a) The parabola opens down and has two zeros.
b) The parabola opens up and has no zeros.
c) The parabola opens down and the vertex is also
the zero of the function.
5. For what value(s) of k will the function
f (x) ⫽ 5x 2 ⫺ 6x ⫹ k have one x-intercept?
6. For what value(s) of k will the function
f (x) ⫽ kx 2 ⫹ 8x ⫹ k have no zeros?
Lesson 3.6 Extra Practice
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