Final Answer:
The graph of g(x)=-3x^2 function is stretched vertically and reflected in the x-axis as compared to the parent function g(x) = x^2, so the correct option is B.
Step-by-step explanation:
To determine which graph is stretched vertically and reflected in the x-axis compared to the parent function g(x) = x^2, let's analyze each option:
A) g(x) = 3x^2
This function represents a vertical stretch of the parent function g(x) = x^2 by a factor of 3 because the original function is multiplied by a constant factor greater than 1.
However, this function is not reflected in the x-axis since the coefficient is positive.
B) g(x) = -3x^2
This function represents both a vertical stretch of the parent function g(x) = x^2 by a factor of 3 and a reflection in the x-axis.
The reflection is indicated by the negative sign, which means the entire graph of x^2 is flipped over the x-axis. The stretch is indicated by the absolute value of the coefficient being greater than 1.
C) g(x) = 1/3x^2
This function represents a vertical compression of the parent function g(x) = x^2 by a factor of 1/3 because the original function is multiplied by a constant factor less than 1.
There is no reflection in the x-axis since the coefficient is positive.
D) g(x) = -1/3x^2
This function represents both a vertical compression of the parent function g(x) = x^2 by a factor of 1/3 and a reflection in the x-axis.
The negative sign indicates the reflection, and the coefficient less than 1 (but positive when reflected) indicates the compression.
Since the question asks for the function that is both stretched vertically (meaning the factor is greater than 1) and reflected in the x-axis (meaning there is a negative sign in front of the coefficient), the correct answer is:
B) g(x) = -3x^2