Question

List the intercepts and test for symmetry.

y^2 - x - 4 = 0

I got (-4,0) and (0,2) for the intercepts.

-y^2 - x - 4 = 0 Is not symmetrical to the x axis, correct?

y^2-(-x) - 4 = 0 Is not symmetrical to the y axis, correct?

-y^2 + x - 4 = 0 Is not symmetrical to the origin, correct?

Answer 1

Since x is in the 1st degree and y is in the 2nd degree, this is an x parabola. So we solve for x and get:

x = y^2 - 4,
We have the difference of 2 squares:
(y + 2) (y - 2) = 0,
y + 2 = 0,
y = -2.

y - 2 = 0,
y = 2.

Solution set: y = -2, and y = 2.
The x parabola is symmetric to the x
axis.

The y-intercepts are -2, and 2.