To graph the function rule y = 6x^2, we need to plot multiple points on a coordinate plane and connect them to form the curve.
Let's choose some x-values and calculate their corresponding y-values:
When x = -2, y = 6(-2)^2 = 6(4) = 24.
When x = -1, y = 6(-1)^2 = 6(1) = 6.
When x = 0, y = 6(0)^2 = 6(0) = 0.
When x = 1, y = 6(1)^2 = 6(1) = 6.
When x = 2, y = 6(2)^2 = 6(4) = 24.
Now, let's plot these points on a coordinate plane:
(-2, 24)
(-1, 6)
(0, 0)
(1, 6)
(2, 24)
Next, we connect the points in the order they were listed:
You should have a symmetrical curve that opens upwards, resembling a "U" shape. The vertex of the parabola is the point (0, 0), and the graph is symmetric about the y-axis.
Here is a rough sketch of the graph:
|
30 -+
|
20 -+
|
10 -+
|
0 -+------------+--------
-2 0 2
Note: This graph is not drawn to scale and is only a rough sketch.
Graph the function rule.
y = 6x^2
3 answers
The amount a basketball coach spends at a sporting goods store depends on the number of basketballs the coach buys. The situation is represented by the function rule a = 17b.
a.
Make a table of values and graph the function rule. Is the graph continuous or discrete? Explain.
b.
Suppose the coach spent $119 before tax. How many basketballs did she buy?
a.
Make a table of values and graph the function rule. Is the graph continuous or discrete? Explain.
b.
Suppose the coach spent $119 before tax. How many basketballs did she buy?
a. To create a table of values, we can choose different values for b and calculate the corresponding values for a using the function rule a = 17b.
Let's choose some values for b: 0, 1, 2, 3, 4.
When b = 0, a = 17(0) = 0.
When b = 1, a = 17(1) = 17.
When b = 2, a = 17(2) = 34.
When b = 3, a = 17(3) = 51.
When b = 4, a = 17(4) = 68.
Now, let's create a table of values:
b | a
-----
0 | 0
1 | 17
2 | 34
3 | 51
4 | 68
To graph the function rule, we plot the points from the table on a coordinate plane:
(0, 0)
(1, 17)
(2, 34)
(3, 51)
(4, 68)
Next, we connect the points in the order they were listed:
The graph represents a continuous line passing through all the points. Therefore, the graph is continuous.
b. If the coach spent $119 before tax, we can plug this value into the function rule and solve for b:
119 = 17b
Divide both sides of the equation by 17:
119/17 = b
b ≈ 7
Therefore, the coach bought approximately 7 basketballs.
Let's choose some values for b: 0, 1, 2, 3, 4.
When b = 0, a = 17(0) = 0.
When b = 1, a = 17(1) = 17.
When b = 2, a = 17(2) = 34.
When b = 3, a = 17(3) = 51.
When b = 4, a = 17(4) = 68.
Now, let's create a table of values:
b | a
-----
0 | 0
1 | 17
2 | 34
3 | 51
4 | 68
To graph the function rule, we plot the points from the table on a coordinate plane:
(0, 0)
(1, 17)
(2, 34)
(3, 51)
(4, 68)
Next, we connect the points in the order they were listed:
The graph represents a continuous line passing through all the points. Therefore, the graph is continuous.
b. If the coach spent $119 before tax, we can plug this value into the function rule and solve for b:
119 = 17b
Divide both sides of the equation by 17:
119/17 = b
b ≈ 7
Therefore, the coach bought approximately 7 basketballs.
1 answer