The parabola defined by y2 equals 4x plus 6?

Answer 1

That would be a horizontal parabola, with it's vertex pointing to the left:

y2 = 4x + 6

y2 - 6 = 4x

x = y2/4 - 3/2

Now let's find it's vertex, by taking it's derivative and finding the point at which it equals 0:

x' = y/2

y = 0

x = 02/4 - 3/2

x = -3/2

So it's vertex occurs at the point (-3/2, 0)

Now let's find out where it intercepts the y-axis:

x = y2/4 - 3/2

0 = y2/4 - 3/2

y2/4 = 3/2

y2 = 6

y = ±√6

So it intercepts the y-axis at the points (0, -|√6|) and (0, +|√6|)