How to solve an equation for a parabola

Question

Find the standard form of the equation of a parabola with a vertex (1,2) and directrix y=1

Answer 1

Draw a picture and you will see that the distance from the vertex to the directrix is .5 as is the distance from the focus to the vertex

Remember the formula 4p(y-k)= (x-h)^2 where h and k are the coordinates of the vertex and p is the distance from the vertex to the focus

So (4)(.5)(y-2)= (x-1)^2

2(y-2)= (x-1)^2

2y -4 = x^2 -2x +1

2y= x^2 -2x +5

y= x/2 -x +5/2