D asked in Science & MathematicsMathematics · 7 years ago

Maths: Polynomial Graphs and Values?

Let f be a quartic polynomial (ie. a polynomial of degree 4). Suppose that f has zeros at -2; 1; 3; 4 and that f (0) = 4.

- Sketch a graph of f.

- If f(x) is written in the form:

f (x) = A(x - a)(x - b)(x - c)(x - d)

then find the values of A; a; b; c; d.

1 Answer

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  • MrsN
    Lv 5
    7 years ago
    Favorite Answer

    Use your graphing calculator or an online graphing calculator like the one at http://my.hrw.com/math06_07/nsmedia/tools/Graph_Ca... to graph the equation y= -1/6*(x+2)*(x-1)*(x-3)*(x-4) and you will see what the graph looks like.

    a, b, c, and d are the zeros of the function listed above: -2, 1, 3, and 4

    So, f(x) = A(x+2)(x-1)(x-3)(x-4).

    I knew that the "A" (constant) in the equation I graphed was -1/6 because f(0)=4, so:

    4=A(0+2)(0-1)(0-3)(0-4)

    4=A(-24)

    -1/6=A

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