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Chapter 11: Problem 72

Explain how to decide whether a parabola opens upward or downward.

Short Answer

Expert verified
The parabola opens upward if the coefficient 'a' (of the x虏 term) is positive, and downward if 'a' is negative in the standard form equation \(y = ax^2 + bx + c\).

Step by step solution

01

Understanding the Standard Form

A parabola can be described by a quadratic equation in the form \(y = ax^2 + bx + c\), where 'a', 'b', and 'c' are constants and 'a' cannot be equal to zero because then the equation will not represent a parabola. This is called the standard form of a quadratic equation.
02

Identifying the coefficient of the \(x^2\) term

Check the coefficient 'a'. The coefficient 'a' is the value in front of the \(x^2\) term in the equation.
03

Deciding the direction of the Parabola

If 'a' is positive, the parabola opens upward. If 'a' is negative, the parabola opens downward. This is an important result from the behaviour of quadratic functions.

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