AFOQT Practice Test

If the absolute value of a in a quadratic equation is less than 1, what happens to the parabola?

1. It becomes narrower

2. It becomes wider

3. It remains unchanged

4. It reflects over the x-axis

The correct answer is: It becomes wider

When the absolute value of "a" in a quadratic equation is less than 1, it affects the width of the parabola. Specifically, a smaller absolute value of "a" indicates that the parabola will become wider. This is because the value of "a" influences the steepness of the parabola. When "a" is less than 1 in absolute terms, the graph is less steep, resulting in a wider appearance. This concept comes from the standard form of a quadratic equation, \(y = ax^2 + bx + c\). When the absolute value of "a" decreases from 1 to a value less than 1, the parabola spreads out horizontally, leading to a larger reach along the x-axis for any given y-value. In contrast, if the absolute value of "a" were greater than 1, the parabola would be narrower and steeper, which visually demonstrates the inverse relationship between the value of "a" and the width of the parabola. Therefore, when analyzing the impact of "a" on the shape of the parabola, a value less than 1 leads to a wide, flatter curve.