For the parabola $y=a{x}^2$, how does the graph change as $\left|a\right|$ increases?

• A. It changes from opening up to opening down.
• B. It becomes narrower (steeper).
• C. It becomes wider (flatter).
• D. It shifts upward.

Answer: (B)

Verified step by step guidance

1. Recall the general form of a parabola: \(y = a x^{2}\), where \(a\) determines the shape and direction of the parabola.
2. Understand that the sign of \(a\) (positive or negative) controls whether the parabola opens upward or downward, but the question focuses on the absolute value \(|a|\).
3. Recognize that as \(|a|\) increases, the parabola becomes steeper or narrower because the \(y\) values grow faster for the same \(x\) values.
4. Conversely, as \(|a|\) decreases (approaches zero), the parabola becomes wider or flatter because the \(y\) values grow more slowly for the same \(x\) values.
5. Therefore, the key effect of increasing \(|a|\) is that the parabola becomes narrower (steeper), without changing its direction of opening.