Algebra 2 Unit 2 Review Name_________________ Date_________________ Period_________________ Simplify each expression. Write the solution in standard form.
1) 7𝑖 + 3 − (7𝑖 − 14)
2) −2 − 8𝑖 + −3 − 2𝑖
3) 2 + 5𝑖 4 − 6𝑖
!!!!
4) !!!!
Given the solutions write the quadratic equation.
5) 𝑥 = 5 𝑎𝑛𝑑 𝑥 = −2
6) Let 𝑚 = 3 − 4𝑖 𝑎𝑛𝑑 𝑛 = −1 + 5𝑖. Graph m and n on the Real-Imaginary plane.
Algebra 2 Unit 2 Review Find the exact solution(s) to the equation using the method of your choice.
7) 𝑥 ! = 10𝑥 − 34
8) 3𝑥 ! + 10 = 4𝑥
9) A carnival game asks participants to strike a spring with a hammer. The spring shoots a ball up
toward a bell. If the ball hits the bell, the participant wins a prize. Suppose that a participant strikes
the spring and shoots the ball according to the model 𝑑 𝑡 = 4𝑡 ! − 24𝑡 + 42, where d is the distance
in feet between the ball and the bell and 𝑡 is the time in seconds since the spring was struck. Will the
participant win the prize? Explain why or why not.
Algebra 2 Unit 2 Review 10) A landscaping company has been hired to build a sidewalk around a small park area, as shown in
the drawing below. The rectangular park is 45 feet by 25 feet. If the total area of the sidewalk is 800
square feet, what is the smallest width (x) that the sidewalk can be?
For questions 11 & 12 use: 𝑓 𝑥 = 𝑥 ! and 𝑔 𝑥 = −4(𝑥 − 3)! − 2
11) What effect do the numerical values in 𝑔 𝑥 have on the original equation 𝑓 𝑥 ?
12) Graph 𝑔 𝑥 and 𝑓 𝑥 on the graph below. 10 5 0 -­‐10 -­‐5 0 5 10 -­‐5 -­‐10 Algebra 2 Unit 2 Review 13) A punter for a football team kicks the ball up into the air. The height of the ball in feet t seconds
after he kicks it can be modeled by the quadratic function ℎ 𝑡 = −16𝑡 ! + 80𝑡.
a) What is the height of the football 2 seconds after the punter kicks it?
b) What is the maximum height the football will reach?
c) How long does it take the ball to hit the ground?