Plotting Cubic Graphs

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

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)

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

Plot a graph of the function: Plotting Cubic Graphs Plot a graph of the function: y = 10 + 19x – 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

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

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

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!

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

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