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Intermediate Algebra

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For the quadratic equation y=(x-3)^2-2. Determine: A) whether the graph opens up or down; B) the y-intercept; C)the x-intercepts; D) the points of the vertex. and D) graph the equation with at lease 10 pairs of points.

  • Intermediate Algebra -

    Vertex Form: Y = a(x-h)^2 + k.

    A. The parabola opens upward because "a"
    is positive.

    B. Y = (x-3)^2 - 2.
    Let X = o and solve for Y:
    Y = (0-3)^2 - 2 = 7. = Y-int.

    C. Let Y = 0 and solve forX:
    Y = (x-3)^2-2 = 0.
    (x-3)^2 = 2
    Take sgrt of both sides:
    x-3 = +-sqrt2
    X = +-1.414 + 3 = 4.14, and 1.59. = X-intercepts.

    D. V(h,k) = V(3,-2).

    E. Select values of X below and above
    h and calculate the corresponding value of Y.

    (x,y). Y = (x-3)^2 - 2.
    (-2,23)
    (-1,14)
    (0,7)
    (1,2)
    (2,-1)
    V(3,-2)
    (4,-1)
    (5,2)
    (6,7)
    (7,14)
    (8,23).

  • Intermediate Algebra -

    for the quadratic equation y=(x-3)^2-2 determine A) weather the graph opens up or down B) the y- intercept; C) the x intercept D) the points of the vertex and E ) graph the equation with at least 10 pairs of points

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