# 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 $x=2$. ## Factorising Monic Quadratic Trinomials Minus Plus Form

Transcript Again I’m going to put x and x on the left-hand side because again x times x is definitely x squared. Now 3, 3…

## Positive Definite Negative Definite

The Discriminant and the Quadratic Graph The discriminant of the quadratic equation $ax^2+bx+c=0$ is $\Delta = b^2-4ac$. We used the discriminant to determine the number…

## Factorising Monic Quadratic Trinomials Minus Minus Form

Transcript Both of them are negative. In this kind of case again you’re going to consider the signs again. Okay? Very very carefully be very…

## Fractions involving Quadratic and Linear Terms: Common Factors

Transcript All right! Again, we’ve got a fraction and you can see we have a quadratic on the numerator. So again our cross method. So…

## Fractions involving Quadratic Terms: Monic Expressions

Transcript The numerator, first of all, I’m going to use x and x because it’s negative. I know I’m going to use positive and a…