Order the group of quadratic functions from widest to narrowest graph.
y = 3x^2;y=5x^2;y=7x^2
Order the group of quadratic functions from widest to narrower graph.
y = -1/3x^2;y=2/3x^2; y = 3/2 x^2
To order the group of quadratic functions from widest to narrowest graph, we need to compare the values of the coefficient in front of x^2 in each equation.
For the first group of equations:
1. y = 3x^2
2. y = 5x^2
3. y = 7x^2
Comparing the coefficients, we can see that the quadratic functions from widest to narrowest graph are:
y = 7x^2, y = 5x^2, y = 3x^2.
For the second group of equations:
1. y = -1/3x^2
2. y = 2/3x^2
3. y = 3/2x^2
Comparing the coefficients, we can see that the quadratic functions from widest to narrowest graph are:
y = 3/2x^2, y = 2/3x^2, y = -1/3x^2.
So, the correct order from widest to narrowest graph for the second group is:
y = 3/2x^2, y = 2/3x^2, y = -1/3x^2.
To determine the order of quadratic functions from widest to narrowest, we need to examine the coefficients of the x^2 terms in each equation.
In the first group of quadratic functions:
y = 3x^2;
y = 5x^2;
y = 7x^2
The coefficients of the x^2 terms are 3, 5, and 7. The coefficient determines the width or narrowness of the graph. The quadratic function with the largest coefficient will have the narrowest graph, while the one with the smallest coefficient will have the widest graph.
So, the order of the functions from widest to narrowest graph is:
y = 7x^2; y = 5x^2; y = 3x^2
Now let's move on to the second group of quadratic functions:
y = -1/3x^2;
y = 2/3x^2;
y = 3/2x^2
Here, the coefficients of the x^2 terms are -1/3, 2/3, and 3/2. Again, the larger the coefficient, the narrower the graph.
To compare these coefficients, it's helpful to find a common denominator:
-1/3 = -2/6;
2/3 = 4/6;
3/2 = 9/6.
Now we can order the functions from widest to narrowest graph:
y = 9/6x^2; y = 4/6x^2; y = -2/6x^2.
However, it's a common practice to simplify the coefficients, so we can further simplify them to get a clearer view:
y = 3/2x^2; y = 2/3x^2; y = -1/3x^2.
So, the order of the functions from widest to narrower graph is:
y = 3/2x^2; y = 2/3x^2; y = -1/3x^2.