UNIT 12 STUDY GUIDE
Answer all questions on a separate piece of paper.
Solving Using Zero Product Property
1. What are the steps to solving using ZPP?
2. Solve the following problems using ZPP:
)(
)
a. (
)(
)
b. (
(
)
c.
d.
e.
f.
Solving Using Square Root Property
1. What are the steps to solving using SRP?
2. Solve the following using SRP.
a.
b.
c.
d.
e.
f.
Solving by Completing the Square
1. What are the steps to solving by completing the square?
2. Complete the square for each expression.
a.
b.
c.
3. Solve the following by completing the square.
a.
b.
c.
Solving Using the Quadratic Formula
1. Write the quadratic formula. What two things should you do first before you start substituting into the quadratic
formula?
2. Solve the following using the Quadratic formula. Be sure the write the formula and the correct substitutions
each time. If applicable, leave answer in radical form (no decimals).
a.
b.
c.
Simplify Complex Numbers (imaginary numbers)
1. Simplify the following complex numbers.
a. √
b. √
c. √
d.
√
The Discriminant
1. Write the formula for the discriminant.
2. Describe, in detail, what the discriminant tells us.
3. Find the number of solutions of each equation using the discriminant.
a.
b.
c.
Applications
1. A book falls from a shelf that is 60 inches above the floor. A model for the height h in feet of an object
dropped from an initial height of h0 feet is h = -16t2 + h0, where t is time in seconds after the object is
dropped. How long does it take for the book to reach the ground?
2. Laura dove into a swimming pool from a 15-foot-high diving board with an initial upward velocity of 8
feet per second. Find the time t in seconds it took Lauren to enter the water Use the equation h = -16t2
+ vt + s, where h is height in feet, t is time in seconds, v is the initial upward velocity in feet per second,
and s is the initial height in feet. (Hint, let h = 0 represent the surface of the pool).
3. Brad tossed a baseball in the air from a height of 6 feet with an initial upward velocity of 14 feet per
second. Enrique caught the ball on its way down at a point 4 feet above the ground. How long was the
ball in the air before Enrique caught it? Use the model of vertical motion from Exercise #3.
4. The length of a Charlotte, North Carolina, conservatory garden is 20 yards greater than its width. The
area is 300 square yards. What are the dimensions?
5. Miko wants to build a toy box for her sister. It is to be 2 feet high, and the width is to be 3 feet less
than its length. If it needs to hold a volume of 80 cubic feet, find the length and width of the box.