Order the group of quadratic functions from widest to narrowest graph.
y = 1/3x^2, y = -9x^2, y = -1/2x^2
To determine the width of a quadratic function, we can focus on the coefficient of the x^2 term. The larger the coefficient, the narrower the graph.
In this case, the three quadratic functions are:
1. y = (1/3)x^2
2. y = -9x^2
3. y = (-1/2)x^2
Comparing the coefficients, we can see that:
The first quadratic function has a coefficient of (1/3), which is smaller than the other two. Therefore, it has the widest graph.
The second quadratic function has a coefficient of -9, which is larger than the first quadratic function but smaller than the third one. Therefore, it has a narrower graph compared to the first one but wider compared to the third one.
The third quadratic function has a coefficient of (-1/2), which is the largest of all three. Therefore, it has the narrowest graph.
Therefore, the order of the quadratic functions from widest to narrowest graph is:
1. y = 1/3x^2
2. y = -9x^2
3. y = -1/2x^2