Quadratics Test Review

xy Linear or Quadratic

xy Linear or Quadratic

xy Linear or Quadratic

4. Linear or Quadratic -3x + 4y = 8 5. Linear or Quadratic y = -5x 2 + 3x – Linear or Quadratic 3x 2 + 5y = 24 11

7. Linear or Quadratic8. Linear or Quadratic 9. Linear or Quadratic

Domain: All real numbers Range: y ≥

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

Domain: All real numbers Range: y ≥

xy y = 2x 2 – 4 Remember, in the calculator you can create the table of values easily. Go to: 1)[ Y = ] and enter your equation 2)[2 nd ] [Graph/Table}

xy y = (-1/3)x 2

xy y = x 2 - 4

1 0 (1, 0) x = a)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. (, ) (, )

a)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. (, ) (, ) 1 -8 x = 1 (1, -8)

a)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. (, ) (, ) 4 -2 (4, -2) x = 4 NONE 18.

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

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

21. One x-intercept

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

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

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

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

_____ 28. Which of the following functions represents a parabola that is narrower than the parent function f(x) = x 2 ? A.f(x) = x B. f(x) = ⅓ x 2 C. f(x) = 3x 2 D. f(x) = x 2 – 3 Remember: The larger the coefficient, the narrower The smaller the coefficient, the wider

_____ 29. How do the graphs of the functions f(x) = x and g(x) = x 2 − 6 relate to each other? A.The graph of f(x) is one unit above the graph of g(x). B.The graph of f(x) is 11 units above the graph of g(x). C.The graph of f(x) is one unit to the right the graph of g(x). D.The graph of f(x) is 11 units to the right the graph of g(x).

_____ 30. When graphed, which function would be shifted 3 units down from the graph of f(x) = x 2 + 6? A.g(x) = x B.g(x) = x C.g(x) = x 2 – 3 D.g(x) = x 2 + 1

_____ 31. Given the function y = x 2 + 3, which describes the shift in the vertex of the parabola if, in the function, 3 is changed to -8? A.5 units down B.5 units up C.11 units up D.11 units down

_____ 32. How would the graph of the function y=x 2 – 4 be affected if the function were changed to y=x 2 + 1? A.The graph would shift 5 units down. B.The graph would shift 5 units up. C.The graph would shift -3 units down. D.The graph would shift 3 units up.

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

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

TimeHeight Scott shot his algebra book using a giant slingshot. The path of the book can be modeled by the function y = -16x x TimeHeight

39.What ordered pair represents when the book reaches its maximum height? ( ___,___) 40.How long did it take for the book to hit the ground? _____________ 41.At what times was the book at 336 feet? _____________ 42.What does the ordered pair (8, 256) represent? __________________________________ seconds 3 and 7 seconds After 8 seconds, the book is 256 feet high