Math - Crossing the X axis problem?

Question

Does the graph y = x^2 cross the x-axis? I know it touches it but can you say it "crossed" the axis?

In other words, what is the definition of "crossing"?

Answer 1

Crossing the x-axis would be defined as y being negative. Because a number's square can never be negative, the graph y=x^2 never crosses the x-axis.

Answer 2

This graph does not cross the x-axis. It intersects the x-axis. The graph of y = x² - 1 crosses the x-axis in two places.

Answer 3

crossing implies that it is negative on one side and positive on the other, which x^2 is not. Imagine crossing the finish line in a race, if you stop midway during the ripping of the ribbon, you have not won the race :D



This phenomenon you have described is called being "tangent" to the x-axis

Answer 4

Its a Parabola.

Open at the top.

Touching the x axis at the point where x = zero and y = zero.

So you could say the x-axis is a tangent at the parabola's lowest point, at coordinates 0,0.

Answer 5

it never goes below the axis, so I would say it didn't actually cross it.