Write the equation of a polynomial function with the given characteristics. Use

Question

Write the equation of a polynomial function with the given characteristics. Use a leading coefficient of 1 or -1 and make the degree of the function as small as possible.
Q) Crosses the x-axis at -4,0, and 2; lies below the x-axis between -4 and 0; lies above the x-axis between 0 and 2 Write the equation of a polynomial function with the given characteristics. Use a leading coefficient of 1 or -1 and make the degree of the function as small as possible.
Q) Crosses the x-axis at -4,0, and 2; lies below the x-axis between -4 and 0; lies above the x-axis between 0 and 2
Q) Crosses the x-axis at -4,0, and 2; lies below the x-axis between -4 and 0; lies above the x-axis between 0 and 2

Explanation / Answer

1st: f(x) = x(x+4)(x-2) or
2nd: f(x) = -x(x+4)(x-2)
Check to see which one has f(-2) < 0 , that is " below the x-axis".

1st equation:
f(-2)= -2(2)(-4)= 16 > 0

2nd equation:
f(-2) =-[-2(2)(-4)] = -16 < 0

So, 2nd equation is the one you want

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