Cubic By: Dylan, Amy, Ally, Nikolos, and Mary-Catherine

What is a Cubic Polynomial?• A polynomial of degree 3.

Example: x^3 - 1, 4x^3 – 100x^2 + x - 6, and m^2n + mn^2 are all cubic polynomials.

How to turn into standard form

• Ex. F(x)=(x-3)^3 +20

(x-3)(x-3)(x-3)

x^3 -9x^2 +27x-27x-27+20

F(x)=x^3 -9x^2 +27x-27x-7

Write out (x-3)^3

Multiply together to get product using distributive form

Combine like terms

You are done!

Practice Problems• 1. F(x)=(x+5)^3 -5 Convert to standard form

(f(x)=ax^3 +bx^2 +cx+d)

• 2. F(x)=x^3 -20 Y-intercept?

• 3. Domain and Range of f(x)=x^3

• 4. Parent function f(x)=x^3G(x)=-(x+4)^3 +2Describe transformations.

F(x)=x^3 +15x^2 +75x+120

y=-20

Domain is all real numbers. Range is all real numbers.

Reflection. Horizontal translation 4 to the left. Vertical translation up 2.

Examples of Cubic Equations• F(x)= (x-2)^3+3 F(x)=x^3 -6x^2

+12x-8

• F(x)= x^3 -7

• F(x)=2x^3+3x^2-11x-6

Matching Game F(x)=x^3 +7

F(x)=x^3 +3

F(x)=Find the equation

F(x)=x^3

Cubic Homework• The Parent Function is f(x)=x^3

• 1. g(x)=(x-2)^3+3 Describe the Transformations.

• 2. What is the domain and range of f(x)=(x+4)^3+1?

• 3. (x-8)^3+999 What is the X intersect?

• 4. (x+2)^3-1 What is the Y intersect?

In Conclusion…• A cubic graph will always have a domain and

range of all real numbers.• Standard form of a cubic equation is ax^3 +bx^2

+cx+d.

• End! Hope you have enjoyed this presentation and you have a lovely day!