Which of the quadratic functions has the narrowest graph?
a. y=-x^2
b. y=1/3x^2
c. y=3x^2
d. y=1/5x^2
the correct answer is c. y=3x^2
i think it is b.
y(kx) compresses the graph by a factor of 1/k
To determine which quadratic function has the narrowest graph, we need to identify the quadratic function with the smallest coefficient for the x^2 term.
Let's analyze each option:
a. y = -x^2: The coefficient for x^2 is -1.
b. y = (1/3)x^2: The coefficient for x^2 is 1/3.
c. y = 3x^2: The coefficient for x^2 is 3.
d. y = (1/5)x^2: The coefficient for x^2 is 1/5.
Now, to compare the coefficients, we need to find a common denominator:
-1 = -5/5
1/3 = 1/3
3 = 15/5
1/5 = 1/5
Now that we have expressed the coefficients with a common denominator, the quadratic function with the narrowest graph is the one with the smallest coefficient. In this case, the function with the smallest coefficient is y = -x^2.
Therefore, option a. y = -x^2 has the narrowest graph.