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the graph of a polynomial function of degree 3 is tangent to the x-axis at (-4,0) and crosses the x-
axis at (4,0). If those are the only zeros of f, write the equation of f.
Solution
as fraph touches at -4,0 there are two equal roots there, so roots are -4,-4 and 4 so
function is (x-4)*(x-(-4))*(x-(-4)) (x-4)*(x+4)*(x+4) x^3 + 4x^2 -16x - 64 f(x) = x^3 + 4x^2 -
16x - 64

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  • 1. the graph of a polynomial function of degree 3 is tangent to the x-axis at (-4,0) and crosses the x- axis at (4,0). If those are the only zeros of f, write the equation of f. Solution as fraph touches at -4,0 there are two equal roots there, so roots are -4,-4 and 4 so function is (x-4)*(x-(-4))*(x-(-4)) (x-4)*(x+4)*(x+4) x^3 + 4x^2 -16x - 64 f(x) = x^3 + 4x^2 - 16x - 64