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.

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  • 7 years ago
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    Well the curve has to go through the x axis at each of the zeros. Now, from -2 to 1 it must go UP to 4 at x = 0. This means the curve must be going negative (pointing downwards) as you go from -2 to larger negative numbers (i.e. smaller numbers). That means the overall coefficient A in front of the equation must be negative.

    To solve for the value of A:

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

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

    -24A = 4

    A = - 1/6

  • 7 years ago

    f(x)=(-1/6)(x-1)(x+2)(x-3)(x-4)

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