we have that
vertex (0,0)
and
focus (2.5, 0)
we know that
vertex and focus lie on same vertical or horizontal line
in this problem
We can see that focus is right of vertex so parabola opens to right. It is horizontal parabola
the equation is of the form
(y-k)²=4a(x-h)
where (h,k)-----> is the vertex
and
a------> distance between vertex and focus
step 1
vertex (h,k)-------> (0,0)
step 2
find the distance a between point (0,0) and (2.5, 0)
a=√[(0-0)²+(2.5-0)²]------> a=√(2.5)²------> a=2.5 units
the equation is
(y-k)²=4a(x-h)------> (y-0)²=4*2.5*(x-0)-------> y²=10x
the answer is
y²=10x
see the attached figure
