Question

Graph the function rule.

y = 6x^2

Answer 1

[AI-generated answer — Bot GPT 3.5]

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.

Answer 2

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?

Answer 3

[AI-generated answer — Bot GPT 3.5]

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.

Answer 4

[AI-generated answer — Explain Bot]

To graph the function rule y = 6x^2, you can follow these steps:

1. Choose a range of x-values: Select a set of x-values that will give you a good representation of the graph. For example, you can use -3, -2, -1, 0, 1, 2, and 3 to start.

2. Substitute the x-values into the equation: For each x-value, substitute it into the equation to find the corresponding y-value.

For example, let's substitute x = -3:
y = 6(-3)^2
y = 6(9)
y = 54

So when x = -3, y = 54.

3. Repeat step 2 for each x-value you selected in step 1.

For example, substituting x = -2 gives y = 24, x = -1 gives y = 6, x = 0 gives y = 0, x = 1 gives y = 6, x = 2 gives y = 24, and x = 3 gives y = 54.

4. Plot the points: On a graph, plot the points you obtained from step 3. The x-values will be on the x-axis, and the y-values will be on the y-axis.

The points we obtained are:
(-3, 54), (-2, 24), (-1, 6), (0, 0), (1, 6), (2, 24), and (3, 54).

5. Connect the points: Use a smooth and continuous curve to connect the points. Since the equation is y = 6x^2, the graph will be a symmetric U-shape, opening upwards.

After connecting the points, you should have a parabolic curve that opens upward.

Note: If you need to plot more points to get a clearer picture of the graph, you can repeat steps 1-4 with additional x-values.