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Chapter 10: Problem 79

If you are given the standard form of the equation of a parabola with vertex at the origin, explain how to determine if the parabola opens to the right, left, upward, or downward.

Short Answer

Expert verified
The direction of a parabola in the vertex form is determined by the coefficient 'a' in the equation. If 'a' is positive, the parabola opens upward when the equation revolves around y or right when it's around x. If 'a' is negative, the parabola opens downward when around y or left when around x.

Step by step solution

01

Identify the form of the equation

Firstly, identify whether the equation is in the format \(y=a(x-h)^2+k\) or \(x=a(y-k)^2+h\). The equation will look similar to one of these patterns. The key is to look at which variable, x or y, is alone on one side of the equation.
02

Identify the coefficient

After identifying the right format, identify the coefficient 'a' in the equation. The coefficient of the square term will tell you the direction in which the parabola opens.
03

Determine the direction

If 'a' is greater than 0 and y is alone on one side, the parabola opens upward. If 'a' is less than 0 and y is alone on one side, the parabola opens downward. If 'a' is greater than 0 and x is alone on one side, the parabola opens to the right. If 'a' is less than 0 and x is alone on one side, the parabola opens to the left.

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