help pls

A quadratic equation has roots 0 and -6 and a maximum at(-3,4). 

how would you find the equation of the relation?

The quadratic equation is in general:
\(\begin{array}{|rcll|} \hline y &=& a\cdot (x-x_1)\cdot (x-x_2) \quad & | \quad x_1 \text{ and } x_2 \text { are roots}\\ \hline \end{array}\)

Let \(x_1 = 0\) and \(x_2 = -6\)

\(\begin{array}{|rcll|} \hline y &=& a\cdot (x-0)\cdot [x-(-6)] \\ y &=& a\cdot x\cdot (x+6) \\ \hline \end{array} \)

The maximum is (-3,4):

\(\begin{array}{|rcll|} \hline y &=& a\cdot x\cdot (x+6) \\ 4 &=& a\cdot (-3)\cdot (-3+6) \\ 4 &=& a\cdot (-3)\cdot 3 \\ 4 &=& a\cdot (-9) \quad & | \quad : (-9)\\ -\frac49 &=& a \\ \mathbf{a} & \mathbf{=} & \mathbf{ -\frac49 } \\ \hline \end{array}\)

The quadratic equation is:

\(\begin{array}{|rcll|} \hline y &=& a\cdot x\cdot (x+6) \quad & | \quad a =-\frac49 \\ y &=& -\frac49\cdot x\cdot (x+6) \\ y &=& -\frac49\cdot (x^2+6x) \\ y &=& -\frac49\cdot x^2 - \frac49\cdot 6x \\ \mathbf{y} & \mathbf{=} & \mathbf{-\frac49 x^2 - \frac83 x} \\ \hline \end{array}\)

see: