Question

Can I have help on this? I need it explained, answered, and graphed.

Answer 1

The x-intercepts are:

`(-2,0),(-1,0),(1,0)`

The y-intercept is:

`(0,6)`

SOLUTION

Problem Statement

The question tells us to graph the following function

`f(x)=-3x^3-6x^2+3x+6`

Step-by-step explanation

1. Create Table of Values:

To plot the function, we need to create a table of values for x and f(x). We shall choose x-values ranging from -3 to 4, with steps of 0.5

The corresponding y-values, can be gotten by substituting the x-values into the function as shown below:

`\begin{gathered} \text{when x = -3} \\ f(-3)=-3(-3)^3-6(-3)^2+3(-3)+6 \\ f(-3)=81-54-9+6 \\ f(-3)=24 \\ \\ \text{when x = -2.5} \\ f(-2.5)=-3(-2.5)^3-6(-2.5)^2+3(-2.5)+6^{} \\ f(-2.5)=46.875-37.5-7.5+6 \\ f(-2.5)=7.875 \\ \\ \text{when x = 2} \\ f(2)=-3(-2)^3-6(-2)^2+3(-2)+6 \\ f(2)=24-24-6+6 \\ f(2)=0 \\ \vdots \\ \text{when x = 4,} \\ f(4)=-3(4)^3-6(4)^2+3(4)+6 \\ f(4)=-270 \end{gathered}`

The calculation gives a brief summary of how the values of table we shall use to plot the graph is obtained.

The Table of values is given below:

2. Plotting the Graph:

After getting the table of values, we simply need to locate each point on the graph and join them using a curve.

The points plotted on the graph are shown below:

After plotting the points as shown in the figure above, we just simply join the points via a curve.

The curve is shown below:

Thus, we can read off the x-intercepts and y-intercept from the graph given above.

x-intercepts are where the graph crosses the x-axis.

y-intercept is where the graph crosses the y-axis

The x and y intercepts are shown below:

Thus, the x-intercepts are:

`(-2,0),(-1,0),(1,0)`

The y-intercept is:

`(0,6)`