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# Cubic Curve Sketching - PowerPoint PPT Presentation

Cubic Curve Sketching. Basic cubic shapes . Unlike quadratics cubic usually have two bumps e.g. But sometimes the have no bumps. y =x 3 -3x 2 +3. y =-x 3 +3x 2 +3. y =x 3. Example: Sketch y=(x-1)(x+2)(x+3). Here are the steps for sketching cubic curves

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### Cubic Curve Sketching

Unlike quadratics cubic usually have two bumps e.g.

But sometimes the have no bumps

y=x3 -3x2 +3

y=-x3 +3x2 +3

y=x3

Here are the steps for sketching cubic curves

Find x intercepts by solving y=0

Find y intercept by putting x=0

Find out what happens as x get very big and very small (Limits)

Solve:

(x-1)(x+2)(x+3)=0

Equate factors to zero

X-1=0

X+2=0

X+3=0

Intercepts are: x=1, x=-2, x=-3

y=(0-1)(0+2)(0+3)

y= -6

If x3 has a positive coefficient (multiplier) then as x -> ∞ y -> ∞

If x3has a negative coefficient then as x -> ∞ y -> - ∞

In our example

y=(x-1)(x+2)(x+3)

The coefficient of x3 is 1 so as x -> ∞ x -> ∞

Here is the final sketch (Limits)

y=(x-1)(x+2)(x+3)