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Chapter 9: Problem 52

What is a parabola? Describe its shape.

Short Answer

Expert verified
A parabola is a two-dimensional, mirror-symmetrical curve, which is approximately U-shaped. The vertex of the parabola is the point at which the parabola's curve is at its sharpest. The direction of the parabola is determined by the sign of the coefficient of the x虏 term in its equation.

Step by step solution

01

Define Parabola

A parabola is a two-dimensional, mirror-symmetrical curve, which is approximately U-shaped when oriented as shown in the diagram, but can be in any orientation in its plane. It fitting any of several superficially different mathematical descriptions which can all be proved to define curves of exactly the same shape.
02

Describe the Shape

The shape of a parabola, when graphed, is a smooth, U-shaped curve that opens either upward or downward. The vertex of the parabola is the point at which the parabola's curve is at its sharpest. The axis of symmetry of the parabola is the line that runs down its 'center'. If the parabola opens upwards, it has a minimum point at the vertex. Conversely, if the parabola opens downwards, it has a maximum point at the vertex.
03

Direction of Parabola

The direction of the parabola (whether it opens upwards or downwards) is determined by the sign of the coefficient of the x虏 term in the equation of the parabola. If the coefficient is positive, the parabola opens upwards; if it is negative, the parabola opens downwards.

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