Graph Cubic Curves
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Question 1 of 2
1. Question
Sketch the graph of the cubic curve for the equation below`y=2(x+1)(x4)(x6)`Hint
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The standard form for graphing a cubic is `y=a(xr)(xs)(xt)`.The sign of `a` in this equation tells us the shape of the graphIn this equation `a=2` which is positive.Therefore this is a positive cubic curve and has the approximate shape shown below:Find the `x`intercepts of the graph by setting `y=0`.`2``(x+1)``(x4)``(x6)``=0`So `x+1=0`, `x4=0` or `x6=0`This means `x=1`, `x=4` or `x=6`.This gives us `x`intercepts `1`, `4` and `6` which we mark on the `x`axisFind the `y`intercepts of the graph by setting `x=0`.`y=2(0+1)(04)(06)``y=2\cdot (1) \cdot (4)\cdot (6)``y=48`This gives us a `y`intercept of `48` which we mark on the `y`axisDraw a positive cubic curve which passes through the intercepts found. 
Question 2 of 2
2. Question
Sketch the graph of the cubic curve for the equation below`y=2(x1)(x+2)(x+4)`Hint
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The standard form for graphing a cubic is `y=a(xr)(xs)(xt)`.The sign of `a` in this equation tells us the shape of the graphIn this equation `a=2` which is negative.Therefore this is a negative cubic curve and has the approximate shape shown below:Find the `x`intercepts of the graph by setting `y=0`.`2``(x1)``(x+2)``(x+4)``=0`So `x1=0`, `x+2=0` or `x+4=0`This means `x=1`, `x=2` or `x=4`.This gives us `x`intercepts `1`, `2` and `4` which we mark on the `x`axisFind the `y`intercepts of the graph by setting `x=0`.`y=2(01)(0+2)(0+4)``y=2\cdot (1) \cdot (2)\cdot (4)``y=16`This gives us a `y`intercept of `16` which we mark on the `y`axisDraw a negative cubic curve which passes through the intercepts found.
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