CAT 4 - A.8(A) Solving Quadratic Equations

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1. Which value of 𝑥 is the solution to this equation?

• 𝑨. −8
• 𝑩. 3
• 𝑪. 1⁄3
• 𝑫. 5

2. What is the solution set for the following equation?

• 𝑭. {−3.5, 1.5}
• 𝑮. {−1.5, 3.5}
• 𝑯. {0.5, 10.5}
• 𝑱. {−10.5, −0.5}

3. What is the positive solution to this equation?

• 𝑨. 2
• 𝑩. 7⁄5
• 𝑪. 2⁄5
• 𝑫. 7

4. What are the solutions to the following equation?

• 𝑭. −17.5 and 0.5
• 𝑮. −33.5 and −15.5
• 𝑯. −14 and 5
• 𝑱. −16 and −2

5. The height, in feet, of a projectile can be modeled by the quadratic function ℎ(𝑡) = −16𝑡² + 40𝑡 + 5, where 𝑡 represents the time in seconds after being thrown in the air. After how many seconds will the projectile be at a height of 26 feet?

• 𝑨. 0.5
• 𝑩. 1.25
• 𝑪. 1.75
• 𝑫. 2.0

6. A supply company manufactures industrial refrigerators. The cost in dollars, or unit cost 𝐶, to make each refrigerator depends on the number of machines made. If 𝑥 refrigerators are made, then the unit cost is given by the function 𝐶(𝑥) = 0.05𝑥² − 32𝑥 + 10295. How many refrigerators are manufactured by the supply company if the unit cost is $6,980?

• 𝑭. 109
• 𝑮. 144
• 𝑯. 118
• 𝑱. 130

7. Which value of 𝑥 is the solution to this equation?

• 𝑨. 𝑥 = 3⁄2
• 𝑩. 𝑥 = 5⁄8
• 𝑪. 𝑥 = −3⁄8
• 𝑫. 𝑥 = 5⁄4

8. What is the positive solution to the following equation? (Just enter the positive number)

9. What is the negative solution to this equation?