Download Module 3 and 4.1 Review

H. Algebra 2
Module 3 and 4.1 Review
Name: _____________________________________________________ Date: ________________________ Hour: ______
3.1 Solving Quadratic Equations by Taking Square Roots
Find the square of each imaginary number.
1. 4𝑖
2. 𝑖√11
3.
𝒊√𝟕
𝟑
Solve each equation by taking square roots. Give exact answers in reduced radical form. Tell
whether the solutions are real or imaginary.
4. 7𝑥 2 − 12 = 0
5. 𝑥 2 + 9 = 3
6. 2(𝑥 2 − 1) = 𝑥 2 − 3
For 7-8, use the equation 𝒉(𝒕) = 𝒉𝟎 − 𝟏𝟔𝒕𝟐, that models the height of an object in feet after
time t in seconds, and 𝒉𝟎 is the object’s initial height in feet.
7. A carpenter dropped a hammer from a rooftop 48 feet above ground. How long did it take for the
hammer to hit the ground?
8. An acorn fell from a branch 20 feet high and landed on a branch 7 feet high. For how many
seconds was the acorn falling?
3.2 Complex Numbers
Simplify each expression.
1. √−25
2. 3√−49
3. −√−81
1
Add, subtract, or multiply the complex numbers.
4. 4𝑖 + (2 + 8𝑖)
5. (2 − 7𝑖) − (5 − 3𝑖)
6. (3 + 𝑖)(1 − 4𝑖)
3.3 Finding Complex Solutions of Quadratic Equations
Solve each by completing the square. Express answers in reduced radical form.
1. 𝑥 2 + 2𝑥 = 3
2. 3𝑥 2 = 8 + 10𝑥
3. −3𝑥 2 + 7𝑥 = −30
4. 4𝑥 2 = −12𝑥 + 4
Use the discriminant to determine the number and type of solutions. (real, non-real)
5. 𝑥 2 − 3𝑥 = −8
6. 𝑥 2 + 4𝑥 = −3
7. 2𝑥(𝑥 − 6) = −18
8. The function ℎ(𝑡) = −9.8𝑡 2 + 45𝑡 + 1.2 models the height in meters of a baseball t seconds after
it is hit straight up in the air with a velocity of 45 m/s. Will a baseball hit straight up with this
velocity hit the root of a batting cage with a maximum height of 64.5 m? Use the discriminant to
explain your answer.
Solve using the Quadratic Formula. Express answers in reduced radical form.
9. 𝑥 2 + 10𝑥 = −9
10. 𝑥 2 + 2𝑥 = −4
11. 𝑥 2 + 5𝑥 = 3
12. 2𝑥 2 + 7𝑥 + 10 = 0
4.1 Circles
Write the standard form equation of each circle.
1. The circle with center C(-3, 2) and radius r = 4.
2. The circle with center C(-4, -3) and containing the point P(2, 5).
Graph each circle after writing the equation in Standard Form. Identify its center and radius.
3. 4𝑥 2 + 4𝑦 2 + 8𝑥 − 16𝑦 + 11 = 0
Center: ____________Radius: _________
4. 𝑥 2 + 𝑦 2 + 4𝑥 + 6𝑦 + 4 = 0
Center: ____________Radius: _________