Answer
Refer to the graph below.
Work Step by Step
Add $3$ to both sides:
$x+3=y^2+8y-3+3
\\x+3=y^2+8y$
Complete the square by adding $(\frac{8}{2})^2=4^2=16$ to both sides of the equation:
$x+3+16=y^2+8y+16
\\x+19=(y+4)^2$
Recall:
The graph of the equation $x-h=(y-k)^2$ is a parabola that opens to the right and whose vertex is at $(h, k)$.
The equation above can be written as:
$[x-(-19) = [y-(-4)]^2$
Thus, its graph is a parabola that opens to the right whose vertex is at $(-19, -4)$.
To graph the given equation, perform the following steps:
(1) create a table of values by assigning values to $x$ then solving for the corresponding value of $y$ for each one.
Refer to the table below.
\begin{array}{cc}
&x &y
\\&-19 &-4
\\&-3 &0
\\&-3 &-8
\end{array}
(2)Plot the points from the table and connect the points using a smooth curve to form a parabola.
Refer to the graph in the answer part above.
