Question

Describe the effect of a negative leading coefficient on x^2. In other words, how is the graph transformed with -ax^2? Why does it have this effect?

Options:
A) The graph is reflected across the x-axis and becomes wider.
B) The graph is reflected across the y-axis and becomes narrower.
C) The graph is reflected across the x-axis and becomes narrower.
D) The graph is reflected across the y-axis and becomes wider.

Answer 1

A negative leading coefficient on x^2 reflects the graph across the x-axis; the width of the graph remains unchanged by the sign of the coefficient. The correct option is B.

Step-by-step explanation:

The effect of a negative leading coefficient on the term x2 is that the graph of the quadratic equation y = -ax2 will be reflected across the x-axis when compared to the graph of y = ax2 where a is positive. This reflection occurs because the negative coefficient essentially multiplies all y-values by -1 for any given x-value, inverting the graph.

The width of the graph (how wide or narrow it appears) is not affected by the sign of a but rather by the absolute value of a; the larger the absolute value of a, the narrower the graph, and vice versa.

Therefore, the correct answer to how the graph is transformed with -ax2 is that it is reflected across the x-axis. However, it does not inherently become wider or narrower due to the negative sign alone. The correct option is B.