Question

How do you determine the equation of a parabola in standard form with a vertex at (3, 4) passing through the point (5.4)?

Answer 1

There is no such parabola.

Explanation:

The vertex represents either the maximum or minimum value of the parabola and has form `(h,k)`. The horizontal line `y=k` intersects the parabola in exactly one point: at the vertex. Since one of your points is the vertex, and has `y`-coordinate `4`, the line `y=4` only intersects the parabola at only that point. Since the other point is `(5,4)`, with `y`-coordinate 4, that point cannot be on the parabola.