AFOQT Practice Test

What happens to the parabola as the absolute value of a increases beyond 1?

1. It becomes wider

2. It remains the same

3. It becomes narrower

4. It flips upside down

The correct answer is: It becomes narrower

As the absolute value of the coefficient 'a' in the equation of a parabola (typically written as \( y = ax^2 \)) increases beyond 1, the parabola becomes narrower. The coefficient 'a' influences the vertical stretch or compression of the parabola. When the absolute value of 'a' is greater than 1, the parabola is compressed vertically, which causes it to appear narrower. This is because the distance between the vertex of the parabola and its points on either side increases more rapidly. Conversely, if the absolute value of 'a' is between 0 and 1, the parabola is wider because it stretches vertically. Therefore, as 'a' increases beyond 1, the path traced by the parabola becomes steeper and more focused, clearly demonstrating the property of becoming narrower. This characteristic is crucial for understanding how changes in the parameters of quadratic equations affect their graphical representations.