Cubic Graph Sketching

Cubic Graph Sketching

Cubic Graph Sketching start considering the \(x\)-intercepts and whether the leading coefficient is either positive or negative.

Question 1

Sketch the graph of \( y=(x-1)(x+2)(x-3) \).

The graph cuts at \( x=1, x=-2, x=3 \).


Question 2

Sketch the graph of \( y=(x^2-2x)(x+3) \).

\( y=(x^2-2x)(x+3) = x(x-2)(x+3) \)
The graph cuts at \( x=0, x=2, x=-3 \).


Question 3

Sketch the graph of \( y=(x+1)(x-2)^2 \).

The graph cuts at \( x=-1 \) and touches \( x=2 \).


Question 4

Sketch the graph of \( y=(x+1)^2(x-2) \).

The graph touches at \( x=-1 \) and cuts \( x=2 \).


Question 5

Sketch the graph of \( y=x^2(x+2) \).

The graph touches at \( x=0 \) and cuts \( x=-2 \).


Question 6

Sketch the graph of \( y=x(x+2)^2 \).

The graph touches at \( x=-2 \) and cuts \( x=0 \).


Question 7

Sketch the graph of \( y=-x^2(x-2) \).

The graph touches at \( x=0 \) and cuts \( x=2 \).


Question 8

Sketch the graph of \( y=(x+1)^2(2-x) \).

\( y=(x+1)^2(2-x) = -(x+1)^2(x-2)\)
The graph touches at \( x=-1 \) and cuts \( x=2 \).


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