Algebra 2 by Richard Wright

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2-Review

Take this test as you would take a test in class. When you are finished, check your work against the answers.

    2-01

    Describe the transformations of the graph.

  1. f(x) = (x − 3)2 + 5
  2. f(x) = −2x2

    3. Graph.

  3. f(x) = (x + 1)2 − 4

    4. Write a quadratic function with the given vertex.

  4. Vertex: (2, −3); Passes through (0, 9)

    5. 2-02

    Identify the vertex.

  5. y = 2(x − 1)(x + 3)
  6. y = x2 + 4x − 5

    7. Graph.

  7. \(y=\frac{1}{2}x^2+x-2\)

    8. Write a quadratic function with the given x-intercepts.

  8. x-intercepts: (3, 0) and (7, 0); Passes through (4, 3)

    9. 2-03

    (a) Is the line of the graph solid or dashed? (b) Is the graph shaded above or below the parabola?

  9. y ≥ −2(x − 4)(x + 1)
  10. y < x2 − 5

    11. Graph.

  11. y > x2 + 2x + 1
  12. \(\left\{\begin{align} y& > \frac{1}{2}(x-1)^2 - 4 \\ y& < -x^2 + 4 \end{align}\right.\)

    13. 2-04

    Describe the end behavior of the graph.

  13. y = −7x4 + 2x2 − 15
  14. y = 2 + 3x + 5x3

    15. (a) Graph the function, (b) estimate the turning points, and (c) estimate the x-intercepts.

  15. \(y=\frac{1}{2}x^3-\frac{1}{2}x^2-x+2\)
  16. y = 0.1x4 − 1.8x2 + 4

    17. 2-05

    Write a polynomial function with the given x-intercepts.

  17. x-intercepts: (2, 0), (1, 0), (−4, 0); passes through: (0, 5)
  18. x-intercepts: (−1, 0), (0, 0), (4, 0); passes through: (1, 2)

    19. Use finite differences to find the degree of the function passing through the given points.

  19. x 0 1 2 3 4 5 6 7
    y 1 −1 −1 1 5 11 19 29
  20. x 0 1 2 3 4 5 6 7
    y 0 −2 −10 −30 −68 −130 −222 −350

Answers

  1. Translated 3 right and 5 up
  2. Reflected over x-axis and vertical stretch by factor of 2
  4. y = 3(x − 2)2 − 3
  5. (−1, −8)
  6. (−2, −9)
  8. y = −(x − 3)(x − 7)
  9. Solid, shaded above
  10. Dashed, shaded below
  13. Falls to the left, falls to the right
  14. Falls to the left, rises to the right
  15. ; Max: (−0.5, 2.3), Min: (1.2, 0.9); x-int: (−1.6, 0)
  16. ; Max: (0, 4), Min: (−3, −4.1), (3, −4.1); x-int: (−3.9, 0), (−1.6, 0), (1.6, 0), (3.9, 0)
  17. \(y=\frac{5}{8}\left(x-2\right)\left(x-1\right)\left(x+4\right)\)
  18. \(y=-\frac{1}{3}\left(x+1\right)\left(x\right)\left(x-4\right)\)
  19. 2
  20. 3