I'm wondering, what differentiates a parabola from a symmetrical U? My friends all have conflicting opinions, so I thought I'd ask here.
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Well, no. A "U" has a curved bottom, and leads to two sides that are vertical. A parabola, X^2, starts at the origin with a slope of zero, and as positive x values increase, the slope keeps increasing, and the parabola gets steeper and steeper. The same happens on the left side of the origin. As negative x values get smaller, the slope gets steeper and steeper, to the point where if you move one unit to the right or left, the Y value changes in the millions. However, a parabola's slope will never be vertical, because a vertical slope is undefined. The slope may get to be a BILLION at some point, but it will never be vertical. Theoretically, if you kept sketching points on a graph for a parabola, the X values go to infinity, so there is no definite width, like a U has. Kinda looks like a U, but not really.