Problem 76
Question
Explain how to decide whether a parabola opens upward or downward.
Step-by-Step Solution
Verified Answer
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.
1Step 1: Identify the Standard Form of a Quadratic Function
The standard form of a quadratic function is \(f(x) = ax² + bx + c\), where 'a', 'b' and 'c' are constants and \(a \neq 0\). It is crucial to identify this form to proceed with the exercise.
2Step 2: 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.
3Step 3: 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.
Other exercises in this chapter
Problem 75
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