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College Algebra

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1.Answer the following for the given quadratic function. f(x) = -2x^2 - 8x - 13
(a) does the graph of f open up or down?
(b) what is the vertex (h,k) of f?
(c) what is the axis of symmetry?
(d) what are the intercepts?
(e) how is the graph suppose to look for this question?
(f) what is the domain of f?
(g) what is the range of f?
(h) on what interval is f increasing?
(i) on what interval is f decreasing?
2. Describe how the graph of h(x) = 1/x + 3 can be obtained from the graph of f(x) = 1/x. Then graph the function h(x).
How can the graph of h(x) = 1/x + 3 be obtained from the graph of f(x) = 1/x?
What is the graph of h(x) = 1/3 + x?

  • College Algebra - ,

    F(x) = -2x^2 - 8x - 13.
    a. Down.

    b. V(h,k).
    h = Xv = -b/2a = 8/-4 = -2.
    k = -2(-2)^2 -8(-2) - 13 = -5.

    c. X = h = -2.

    d. The graph opens downward and k is less than 0. Therefore, there are no
    Intercepts(real solutions).

    e. The graph opens downward and does not
    cross the x-axis.

    f.

    g.

    h. -2 > X = -2.

    i. -2 = X > -2.

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