Answer
$a=1$ or $a=-4$
Work Step by Step
If a point is on the graph, the $(x,y)$ coordinates satisfy the equation.
Here, $(a,4)$ is on th graph, therefore we should plug in these values into the given equation to obtain:
:
$y=x^2+3x$
$4=a^2+3a$
$0=a^2+3a-4$
By using the quadratic formula:
$a_{1,2}=\dfrac{-3\pm\sqrt{3^2-4(1)(-4)}}{2(1)}=\dfrac{-3\pm\sqrt{9+16}}{2}=\dfrac{-3\pm5}{2}$
$a_1=\frac{-3+5}{2}=1$
$a_2=\frac{-3-5}{2}=-4$
The points $(-4,4)$ and $(1,4)$ are on the graph.
