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Quadratic Equations and Functions Practice & Solutions

Solve various quadratic equations and explore functions in this comprehensive math practice set. Find solutions, zeros, factors, and maximum heights in different scenarios. Understand vertex form, completing the square, and interpreting quadratic expressions in real-world situations. Brush up your algebra skills with step-by-step solutions and explanations.

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Quadratic Equations and Functions Practice & Solutions

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  1. 1. Solve 9x2+ 16 = 0 for x.

  2. 2. The function h(t) = 4t2– 12t + 25 represents the height, in inches, of a swing after t seconds, for 0 ≤ t ≤3. a. Solve the function when h(t) = 0. b. Will the swing touch the ground?Explain how you know.

  3. 3. What are the solutions to the equation 12x2= –300?

  4. 4. What are the solutions to the equation 2x2+ 3x + 9 = 0?

  5. 5. Factor the expression 16a4– 81.

  6. 6. Write f(x) = 2x2+ 6x + 1 in vertex form

  7. 7. The expression ??is used to calculate the area of a square, where s is the side length of the square. What does the expression (8x)2 represent? A. the area of a square with a side length of 8 B. the area of a square with a side length of 16 C. the area of a square with a side length of 4x D. the area of a square with a side length of 8x

  8. 8. The function h(t) = –t2+ 8t + 2 represents the height, in feet, of a stream of water being squirted out of a fountain after t seconds. What is the maximum height of the water?

  9. 9. What are the zeros of the function represented by the quadratic expression 2x2+ x – 3?

  10. 10. Factor the quadratic equation x2+ 8x – 30 by completing the square.

  11. 11. The expression –X2+ 70x – 600 represents a company’s profit for selling x items. For which number(s) of items sold is the company’s profit equal to $0? A. 0 items B. 35 items C. 10 items and 60 items D. 20 items and 30 items

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