Question

draw the following parabola:
a. principal axis parallel to x; LR=1; passing through (3,1) and (-5,5); opens to the right.

b. principal axis parallel to x; passing through (0,4), (0,-1) and (6,7)

Answer 1

You know that for the parabola

y^2 = 4px
It opens to the right
The LR is 4p

(So, if the shifted parabola is

(y-k)^2 = 4p(x-h), our points and LR say
(1-k)^2 = (3-h)
(5-k)^2 = (-5-h)
so, the parabola is
(y-4)^2 = (x+6)
So, now you have a 3rd point: the vertex at (-6,4)

Now it's easy to plot the parabolas, using the three points for each.