Question

How do you find the Equation in factored form????

Answer 1

without too much fuss, Check the picture below.

so we have roots at -5 and 1, and a point, incidentally the vertex, at (-2 , 9)

`\begin{cases} x = -5 &\implies x +5=0\\ x = 1 &\implies x -1=0\\ \end{cases} \\\\[-0.35em] ~\dotfill\\\\ \stackrel{original~polynomial}{a ( x +5 )( x -1 ) = \stackrel{0}{y}}\hspace{5em}\textit{we also know that } \begin{cases} x=-2\\ y=9 \end{cases} \\\\\\ a ( -2 +5 )( -2 -1 ) = 9\implies -9a=9\implies a=\cfrac{9}{-9}\implies a=-1 \\\\[-0.35em] ~\dotfill\\\\ ~\hfill {\Large \begin{array}{llll} -( x +5 )( x -1 ) =y \end{array}}~\hfill`