Question 45848
determine the standard equation for a parabola with vertex(2,1) and y intercept (0,3).
Assuming you want the equation of the parabola that opens up
you have the standard vertex form of 4p(y-k)=(x-h)^2
We know h and k and need to find p, as follws:
4p(y-1)=(x-2)^2
Since the parabola passes through (0,3) we have:
4p(3-1)=(0-2)^2
4p(2)=4
p=1/2
The equation you want is 2(y-1)=(x-2)^2
This is standard vertex form.
You may want another form but you can manipulate this
to get the form you want.

Cheers,
Stan H.