Question

Find a polynomial of least possible degree having the graph shown. use a leading coefficient of 1 or -1 .

Answer 1

This function is a polinomial of 4 degrees, and we know that the intercept with the x axis are: -3 and 5 and this are the vertex so the equation will be:

$y=a(x+3)(x+3)(x-5)(x-5)$

and to find the value of the constant a we replace one coordinate so I replace (0,-100) so:

$\begin{gathered} -100=a(0+3)(0+3)(0-5)(0-5) \\ -100=225a \\ a=-\frac{100}{225} \\ a=0.44 \end{gathered}$

So the equation is:

$y=0.44(x+3)^2(x-5)^2$