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Math Help - f(x)

  1. #1
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    f(x)

    Let f(x) = x^2 - 3x - 4.

    a.) Find the slope, m(h), of the secant line between the points A(1, f(1)) and B(1 + h, f(1 + h)).

    *Here's what I've come up with so far.

    f(1) = 1^2 - 3(1) - 4
    f(1) = -6
    So, A is the point (1, -6)

    f(1 + h) = (1 + h)^2 - 3(1 + h) - 4
    f(1 + h) = 1 + 2h + h^2 - 3 - 3h - 4
    f(1 + h) = h^2 - h - 6
    So, B is the point (1 + h, h^2 - h - 6)
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  2. #2
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    Quote Originally Posted by Mr_Green View Post
    Let f(x) = x^2 - 3x - 4.

    a.) Find the slope, m(h), of the secant line between the points A(1, f(1)) and B(1 + h, f(1 + h)).

    *Here's what I've come up with so far.

    f(1) = 1^2 - 3(1) - 4
    f(1) = -6
    So, A is the point (1, -6)

    f(1 + h) = (1 + h)^2 - 3(1 + h) - 4
    f(1 + h) = 1 + 2h + h^2 - 3 - 3h - 4
    f(1 + h) = h^2 - h - 6
    So, B is the point (1 + h, h^2 - h - 6)
    Hello,

    all your calculations are correct.

    Now use the formula to calculate the slope between 2 points P_1(x_1, y_1) \text{ and } P_2(x_2, y_2)

    m=\frac{y_2 - y_1}{x_2 - x_1} Plug in the coordinates you know:

    m=\frac{(h^2 - h - 6) - (-6)}{(1 + h) - 1}=\frac{h^2 - h }{ h}=\frac{h(h - 1) }{ h}=h-1

    EB
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