Final answer:
The narrowest graph out of the options is Option A, y = -3x^2, because its coefficient has the largest absolute value, which means the graph is steeper and narrower. So, the correct answer is A. y = -3x^2.
Step-by-step explanation:
The question asks which of the following quadratic equations has the narrowest graph.
y = -3x^2
y = 1/7x^2
y = 1/3x^2
y = 1/3x^2
The width of the graph of a quadratic equation, generally given in the form y = ax^2, is inversely related to the absolute value of the coefficient a. The larger the absolute value of a, the steeper and narrower the graph will be.
Comparing the absolute values of the coefficients in each of the given options, we find that:
|-3| = 3
|1/7| is approximately 0.14
|1/3| is approximately 0.33
Option A has the largest absolute value of the coefficient. Therefore, y = -3x^2 (Option A) has the narrowest graph among the given equations.