Algebra 2: Chapter 5

Critical Thinking Problems5.1-5.3

1. Give an example of a quadratic function that has a maximum value.

How do you know that it has a maximum?

2. Is it relevant to talk about the maximum or minimum of a linear function?

Why or why not?

3. A quadratic function has values f(-4) = -11, f(-2) = 9, and f(0) = 5. Between which two x values must it have a zero?

Explain your reasoning.

4. Write f(x) = 3x2 – 24x + 50 in vertex form.

5. Use the Zero-Product Property to show that f(x) = ax2 + bx, where a ≠ 0, has two zeros, namely 0 and –b/a.

6. What do you know about the factors of x2 + bx + c when c is positive? When c is negative? What information does the sign of b give you in each case?

7. A soccer ball is kicked from the ground, and its height in meters above ground is modeled by the function h(t) = -4.9t2 + 19.6t, where t represents the time in seconds after the ball is kicked. How long is the ball in the air?

8. The area of a circle is given by A = πr2, where r is the radius. If the radius of a circle is increased by 4 inches, the area of the resulting circle is 100π square inches. Find the radius of the original circle.