Take into account that in a general way, a parabola can be written as follow:
y = a(x - h)^2 + k
where,
a: is the leadding coefficient
(h,k): vertex of the parabola
In order to graph the parabola, first calculate the value of a, by using the following information:
(h,k) = (0,-2)
(x,y) = (5,8)
Replace the previous values into the equation of the parabola and solve for a:
[tex]\begin{gathered} 8=a(5-0)^2-2 \\ 8=25a-2 \\ a=\frac{8+2}{25}=\frac{10}{25}=\frac{2}{5} \end{gathered}[/tex]
Then, the equation of the given parabola is:
[tex]\begin{gathered} y=\frac{2}{5}(x-0)^2-2 \\ y=\frac{2}{5}x^2-2 \end{gathered}[/tex]
Another point could be:
x = -2
[tex]\begin{gathered} y=\frac{2}{5}(-2)^2-2 \\ y=\frac{2}{5}(4)-2 \\ y=\frac{8}{5}-2 \\ y=-\frac{2}{5} \end{gathered}[/tex]
the point is (-2,-2/5).
Then, the graph is:
