# 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 $x=2$.