Answer
$a=-1$ or $a=-5$
Work Step by Step
If a point is on the graph, the $(x,y)$ coordinates satisfy the equation.
Here, $(a,-5)$ is on the graph, therefore we should plug in these values into the given equation to obtain:
$y=x^2+6x$
$-5=a^2+6a$
$0=a^2+6a+5$
By using the quadratic formula:
$a_{1,2}=\dfrac{-6\pm\sqrt{6^2-4(1)(5)}}{2(1)}=\dfrac{-6\pm\sqrt{36-20}}{2}=\dfrac{-6\pm4}{2}$
$a_1=\dfrac{-6+4}{2}=-1$
$a_2=\dfrac{-6-4}{2}=-5$
The points $(-1,-5)$ and $(-5,-5)$ are on the graph.
