Question 824702
Substitution Method: 
1. Solve one equation for one of the variables.
Solving the first equation for x (by dividing each side by 4:
{{{y^2/4 = x}}}
2. Substitute for the solved-for variable in the other equation:
(y^2/4)^2 = 64y
3. Solve the one-variable equation:
{{{y^4/16 = 64y}}}
Multiply by 16 to eliminate the fraction:
{{{y^4 = 1024y}}}
Subtract 1024y (to get a zero on one side):
{{{y^4 - 1024y= 0}}}
Factor out the GCF of y:
{{{y(y^3 - 1024)= 0}}}
Zero Product Property:
{{{y = 0}}} or {{{y^3-1024 = 0}}}
Solving the second equation...
{{{y = 0}}} or {{{y^3=1024}}}
{{{y = 0}}} or {{{y=root(3, 1024) = root(3, 512*2) = root(3, 512)*root(3, 2) = 8root(3, 2)}}}
4. Use the solution(s) to the one-variable equation to find the solution(s) for the other variable:
For y = 0:
{{{(0)^2 = 4x}}}
so x = 0, making (0, 0) a point of intersection.
For {{{y = 8root(3, 2)}}}
{{{(8root(3, 2))^2 = 4x}}}
{{{64root(3, 4) = 4x}}}
{{{16root(3, 4) = x}}}
making ({{{16root(3, 4)}}}, {{{8root(3, 2)}}}) a second point of intersection. Here's a graph to illustrate:
{{{graph(600, 600, -10, 30, -10, 30, sqrt(4x), -sqrt(4x), x^2/64)}}}
(Don't mind the colors.)