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Chapter 3: Problem 76

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

Short Answer

Expert verified
The direction of the opening of a parabola is determined by the sign of the leading coefficient in the standard form of a quadratic function. If the leading coefficient is positive, the parabola opens upwards. If it is negative, the parabola opens downwards.

Step by step solution

01

Identify the Standard Form of a Quadratic Function

The standard form of a quadratic function is \(f(x) = ax虏 + bx + c\), where 'a', 'b' and 'c' are constants and \(a \neq 0\). It is crucial to identify this form to proceed with the exercise.
02

Analyze the leading coefficient

The leading coefficient is the value 'a' in the standard form of the quadratic function. The sign of 'a' determines whether the parabola opens upward or downward.
03

Decide the Opening of the Parabola

If the leading coefficient 'a' is positive, then the parabola opens upwards. Conversely, if 'a' is negative, then the parabola opens downwards.

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Most popular questions from this chapter

Determine whether each statement makes sense or does not make sense, and explain your reasoning. I must have made an error when graphing this parabola because its axis of symmetry is the \(y\) -axis.

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