1. Plotting Cubic Graphs

2. Starter
1) Complete the table of values and plot the graph of y = x2 – 3x – 7 for the range given. You may use a calculator.
2) Complete the table of values and plot the graph of y = 2 – x – x2 for the range given. You may use a calculator. x -3 -2 -1 1 2 3 x -3 -2 -1 1 2 3 y 11 3 -3 -7 -9 -9 -7 y -4 2 2 -4
-10 1 2 3 -1 -2 -3 10
-10

3. Plotting Cubic Graphs We have seen how to plot graphs before
Today we will focus on plotting cubic graphs
You have seen that graphs with an x2 in will take a u or n shape depending on whether the x2 term is positive or negative
Cubic graphs are very important as they allow us to model 3D problems (we will see examples of this next lesson)

4. Plot a graph of the function:
Plotting Cubic Graphs 20 1 2 3 -1 -2 -3
-20
Plot a graph of the function:
y = x3 – x2 - 4x + 4
in the range -3 ≤ x ≤ 3
Using a calculator is fine, but ensure you use brackets when substituting numbers in… x -3 -2 -1 1 2 3 y
-20 6 4 10
𝑦= 𝑥 3 − 𝑥 2 −4𝑥+4
Sub in -3 using brackets
𝑦= (−3) 3 − −3 2 −4 −3 +4
Calculate
𝑦=−20

5. Plot a graph of the function:
Plotting Cubic Graphs
Plot a graph of the function:
y = x – 4x2 – 4x3
in the range -3 ≤ x ≤ 3
Using a calculator is fine, but ensure you use brackets when substituting numbers in… 75 x -3 -2 -1 1 2 3 y 25
-12 -9 10 21
-77 -3 -2 -1 1 2 3
𝑦=10+19𝑥− 4𝑥 2 − 4𝑥 3
Sub in -3
𝑦=10+19 −3 −4 −3 2 −4 (−3) 3
Calculate
𝑦=25
-75

6. Online source of these examples
Plenary
Match up the graphs with the equations. Make sure you can explain your reasoning!
𝑦=2 𝑥 3 −4 𝑥 2 +1
𝑦= 𝑥 3
𝑦= 𝑥 2
𝑦=2𝑥+1
𝑦= 𝑥 2 −4
𝑦= 2−3𝑥−2𝑥 2
𝑦=𝑥
𝑦=3𝑥− 𝑥 3
𝑦=1−0.25𝑥

7. Plenary x -x x2 -x2 -x3 x3 As a general summary:
The graph will always take the general shape of the HIGHEST power in the equation! x3

8. Summary We have learnt how to plot cubic graphs
We have also learnt to recognise their shapes alongside other types of graph we know
Next lesson we will be looking at applications of cubic graphs!

9. Starter (printout)
1) Complete the table of values and plot the graph of y = x2 – 3x - 7. You may use a calculator.
2) Complete the table of values and plot the graph of y = 2 – x – x2 for the range given. You may use a calculator. x -3 -2 -1 1 2 3 x -3 -2 -1 1 2 3 y y 10 10 -3 -2 -1 1 2 3 -3 -2 -1 1 2 3
-10
-10

10. Plenary (printout)
Match up the graphs with the equations. Make sure you can explain your reasoning!
𝑦=2 𝑥 3 −4 𝑥 2 +1
𝑦= 𝑥 3
𝑦= 𝑥 2
𝑦=2𝑥+1
𝑦= 𝑥 2 −4
𝑦= 2−3𝑥−2𝑥 2
𝑦=𝑥
𝑦=3𝑥− 𝑥 3
𝑦=1−0.25𝑥