Name: _____________________________________ Date: ____________________ Period: ______ Algebra 2H

Quadratics Test Review (Sections 4.1-4.6, 4.8)

Note: Make sure you can do these problems without having to think too much about how to start. Make sure to use interval notation where appropriate.

1. Solve each equation by factoring.

a. 25x2 – 144 = 0 b. 6x2 – x – 12 = 0

2. Simplify completely. Given answers in standard form (a + bi). a. (8 + i)2 b. 7i7 + 6i6 – i + 4i400

c. (1 + 2i)3 d. +5

3

i

i

3. Solve using the quadratic formula. Give answers in simplest form.

a. x2 – 4x = 8 b. 4x2 – 4x + 5 = 0

4. Solve 2x2 + 8x = 5 by completing the square. Give answer in simplest form.

5. Solve 9x2 + 4 = 0 by factoring over the complex numbers.

6. Solve (x + 1)2 – 4 = –20 using any method.

7. Determine if the function f(x) = 8x2 – 16x + 4 has a minimum or maximum value, and find the value. Then, state the domain and range of the function.

8. Find the discriminant of each equation. Then, write everything that it tells you about the equation.

a. x2 – 2x = 17 b. 8x2 + 1 = 4x c. 9x2 – 24x + 16 = 0 9. Solve –4 = –x2 – 6x – 9 by graphing.

10. Solve x2 + 6x + 9 < 0 using any method.

11. Find the value of c so that 0 = 2x2 + 4x + c has two imaginary solutions. 12. Calculators are sold to students for $20 each. Three hundred students are willing to buy them at that price. For

every $5 increase in price, there are 30 fewer students willing to buy the calculator. What selling price will produce the maximum revenue and what will the maximum revenue be?

13. At a basketball game, t-shirts are shot from a “t-shirt launcher” into the crowd. The t-shirts are released from a

height of 6 feet with an initial upward velocity of 44 feet/sec. If you catch a t-shirt at your seat 30 feet above

the court, how long was it in the air before you caught it? What is the maximum height that the t-shirt will

reach? Use the model h(t) = –16t2 + v0t + h0, where v0 is the initial velocity and h0 is the initial height.