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Quadratics Test Review

This test review covers linear and quadratic equations, including finding maximum and minimum values, identifying roots, and analyzing the vertex. It also includes questions about shifting graphs and identifying the narrowest and widest functions.

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Quadratics Test Review

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  1. Quadratics Test Review

  2. 1. Linear or Quadratic +2 +20 +40 0 +2 -20 +40 0 +2 -60 +40 0 +2 -100

  3. 2. Linear or Quadratic +1 +14 +1 +14 +1 +14 +1 +14

  4. 3. Linear or Quadratic +1 -12 +8 0 +1 -4 +8 0 +1 +4 +8 0 +1 +12

  5. 4. Linear or Quadratic 1 1 -3x + 4y = 8 5. Linear or Quadratic y = -5x2 + 3x – 17 6. Linear or Quadratic 3x2 + 5y = 24

  6. 7. Linear or Quadratic 8. Linear or Quadratic 9. Linear or Quadratic

  7. Domain: All real numbers Range: y ≥ -4 10.

  8. Domain: All real numbers Range: y ≤ 9 11.

  9. Domain: All real numbers Range: y ≥ -8 12.

  10. 13. y = 2x2 – 4 • Remember, in the calculator you can create the table of values easily. • Go to: • [ Y = ] and enter your equation • [2nd ] [Graph/Table}

  11. 14. y = (-1/3)x2

  12. 16. y = x2 - 4

  13. 16. • 1 0 • (1, 0) • x = 1 • 1 0 • Label and give the ordered pair of the vertex.( , ) • b) Is the vertex the maximum or the minimum? • c) Draw and give the equation of the axis of symmetry. • Equation: _____________ • d) Identify the roots. • ( , ) ( , )

  14. 17. • 1 -8 • x = 1 • (1, -8) • -3 0 5 0 • Label and give the ordered pair of the vertex.( , ) • b) Is the vertex the maximum or the minimum? • c) Draw and give the equation of the axis of symmetry. • Equation: _____________ • d) Identify the roots. • ( , ) ( , )

  15. 18. • 4 -2 • (4, -2) • x = 4 • NONE • Label and give the ordered pair of the vertex.( , ) • b) Is the vertex the maximum or the minimum? • c) Draw and give the equation of the axis of symmetry. • Equation: _____________ • d) Identify the roots. • ( , ) ( , )

  16. 19. Vertex: (2, 4) and two zeros

  17. 20. Vertex: (2, 4) and no roots

  18. 21. One x-intercept

  19. 22. y = 5x2 + 3 Domain: {-3, 1, 3, 5} Range: 48 8 48 128 {8, 48, 128} 5(-3)2 + 3 = 5(1)2 + 3 = 5(3)2 + 3 = 5(5)2 + 3 = • OR you could create the table of values in the calculator • Go to: • [ Y = ] and enter your equation • [2nd ] [Graph/Table}

  20. 23. y = -2x2 + 4x – 7 Domain: {-1, 0, 3, 4} Range: {-23, -13, -7}

  21. 24. y = -17x + 8 Domain: {0, 1, 2, 5} Range: {-77, -26, -9, 8}

  22. 25. f(x) = 4x – 1 f(-3) = 26. f(x) = 2x² – 16 f(-2) = 4(-3) – 1 f(-3) = -13 2(-2)² – 16 f(-2) = -8 27. f(x) = (1/3)x² + 9 f(6) = (1/3)(6)² + 9 f(6) = 21

  23. _____ 28. Which of the following functions represents a parabola that is narrower than the parent function f(x) = x2 ? • f(x) = x2 + 3 B. f(x) = ⅓ x2 • C. f(x) = 3x2 D. f(x) = x2 – 3 Remember: The larger the coefficient, the narrower The smaller the coefficient, the wider

  24. _____ 29. How do the graphs of the functions • f(x) = x2 + 5 and g(x) = x2 − 6 relate to each other? • The graph of f(x) is one unit above the graph of g(x). • The graph of f(x) is 11 units above the graph of g(x). • The graph of f(x) is one unit to the right the graph of g(x). • The graph of f(x) is 11 units to the right the graph of g(x).

  25. _____ 30. When graphed, which function would be shifted 3 units down from the graph of f(x) = x2 + 6? • g(x) = x2 + 9 • g(x) = x2 + 3 • g(x) = x2 – 3 • g(x) = x2 + 1

  26. _____ 31. Given the function y = x2 + 3, which describes the shift in the vertex of the parabola if, in the function, 3 is changed to -8? • 5 units down • 5 units up • 11 units up • 11 units down

  27. _____ 32. How would the graph of the function y=x2 – 4 be affected if the function were changed to y=x2 + 1? • The graph would shift 5 units down. • The graph would shift 5 units up. • The graph would shift -3 units down. • The graph would shift 3 units up.

  28. 33. Order the functions from narrowest to widest. f(x) = - ½ x2 , g(x) = 3x2 , h(x) = -2x2 g(x) = 3x2 , h(x) = -2x2, f(x) = - ½ x2 34. How do the graphs of the functions f(x) = x2 − 4 and g(x) = x2 + 2 relate to each other? f(x) is 6 units below g(x) OR g(x) is 6 units above f(x)

  29. Write the equation of the function that is shifted 3 units above the function y = x2 + 2. • y = x2 +5 • Describe the change from the parent function • y = x2 to y = 5x2 – 8. • y = 5x2 – 8 is narrower and is 8 units below y = x2

  30. Scott shot his algebra book using a giant slingshot. The path of the book can be modeled by the function y = -16x2 + 160x. 37. 38. 400 360 320 280 240 200 160 120 80 40

  31. What ordered pair • represents when the book • reaches its maximum • height? ( ___,___) • How long did it take for • the book to hit the ground? • _____________ • At what times was the • book at 336 feet? • _____________ • What does the ordered pair (8, 256) represent? • __________________________________ 5 400 400 360 320 280 10 seconds 240 200 160 120 3 and 7 seconds 80 40 After 8 seconds, the book is 256 feet high

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