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Algebra 2: Chapter 5 Critical Thinking Problems 5.1-5.3 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. – 24x + 50 in vertex form. 4. Write f(x) = 2 3x 5. Use the Zero-Product Property to show that 2 f(x) = ax + bx, where a ≠ 0, has two zeros, namely 0 and –b/a. 6. What do you know about 2 the factors of x + 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.