Cube Roots and Graphing Cube Roots

​Cube Roots Functions and Graphing Cube Roots

Integrated Math III

Multiple Select

Benchmark Question 4 out 7 got this correct

A number can be expressed as the sum of two cubes. It can be factored, as shown by the polynomial identity below:

$$x^3+\ y^3\ =\ \left(x+y\right)\ \left(x^2-xy+y^2\right)$$  

Which of the following best demonstrates this identity?

• $$15\ =\ 4^3+\ 1^3\ =\ 5\ x\ 3$$  

• $$91\ =\ 4^3\ +\ 3^3\ =\ 6\ x\ 13$$  

• $$126\ =\ 5^3\ +\ 1^3\ =\ 6\ x\ 21$$  

• $$152\ =\ 5^3\ +\ 3^3\ =\ 4\ x\ 38$$  

​Warm UP

Meet the Cube Roots

• Domain: All Real Numbers

• Range: All Real Numbers

• Looks Like a "s"

• a = steepness of the "s" and in front of the coefficient tells us positive or negative.

• h = (x value )tells us going left or right.

• k = (y value) shifts the graph up or down.​

Multiple Choice

What number represents the h in this cubic function?

$$y\ =\ 4\sqrt[3]{x+2}-8$$  

• 4

• 3

• 2

• -8

Multiple Choice

Which number represents the "a" in this cubic function?

$$y\ =2\ \sqrt[3]{x\ -2}+5$$  

• 2

• -2

• 3

• 5

Poll

Does the function shown have a + or - in front of the equation?

• +

• -

Multiple Choice

How to you think the graph compares to the parent function?

• Right 5, Down 2

• Left 5, Down 2

• Right 2, Up 5

• Left 2, Up 5

Graphing Cubic

Functions

​What do you notice about each graph?

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These functions have either an H or K, if you do not see either an H or K it assumed that it is 0.​

​What is the h, k of each function?

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What do you notice about each graph?​

Writing a cubic function given a graph

Multiple Choice

What is the cubic function of this graph?

• $$y\ =\ 3\sqrt[3]{x+2}-1$$  

• $$y\ =\ \sqrt[3]{x+2}-1$$  

• $$y\ =\ \sqrt[3]{x-2}+1$$  

• $$\ y\ =\ 3\sqrt[3]{x-2}+1$$  

Multiple Choice

Which is the cubic function of the graph?

• $$y\ =\ 3\sqrt[3]{x-2}-2$$  

• $$y\ =3\sqrt[3]{x+2}-2$$  

• $$y\ =\ 3\sqrt[3]{x+2}+2$$  

• $$y\ =\ \sqrt[3]{x+2}-2$$  

​EXIT TICKET

​There is a standard form of a cubic function

GOOGLE Cubic Function and on an index card

write the standard form of a cubic function.

​Then, find an example of a cubic function​

here is one website you can use​

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https://www.storyofmathematics.com/solving-cubic-equations/

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