Basics of Cubic Graph Sketching

Cubic Graph Sketching start considering from the $x$-intercepts and whether the leading coefficient is either positive or negative.

Question 1

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

Question 2

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

Question 3

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

Question 4

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

Question 5

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

Question 6

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

Question 7

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

Question 8

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