Question

If you are given a graph of a parabola without an equation, how do you find the parametric equation and draw the curve for it?

Answer 1

A parabola has general equation y^2=4ax for symmetry over the x axis, or x^2=4ay with the y axis as axis of symmetry (that is sitting on the axes like a bowl).

Parametric specification of a parabola:

for y^2=4ax, x=at^2 and y=2at
for x^2=4ay, x=2at y=at^2

If you are given a graph, the first thing to do is determine which axis is the axis of symmetry, then apply the appropriate rule (discussed above). If you are given any point on the curve you can plug this into the equation and determine your a value.

I'm not sure what you mean by drawing the parametric equation- It should give the same parabola as the one you are given if your parametric specs are correct...?

Answer 2

thank you! I'm going to try this and see if i get the answer they are looking for!

Answer 3

no problem, hope it helps.

Answer 4

basically, the question gave a graph of a parabola and then 4 other graphs that were weird looking functions and the question said: Match the graphs of the parametric equations x = f(t) and y = g(t) in (a) − (d) with the parametric curves labeled I−IV.

I'll see if your method works!