Question

What is an equation of a parabola with the given vertex and focus? vertex 0,0 focus 2.5 0?

Answer 1

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