Cubic Functions and Their Properties

This video tutorial explains how to write a cubic function or equation given a problem or a graph. It begins with a review of cubic functions, including their parent graph and equation in graphing form. The tutorial then provides three examples, each demonstrating how to solve for the variable 'a' in a cubic equation. The first example uses a given vertex and point, the second example uses different points, and the third example solves without given points or vertex. The video encourages viewers to pause and try solving the problems independently.

What is the primary focus of this video tutorial?

• Writing cubic functions or equations

• Understanding trigonometric identities

• Graphing linear functions

• Solving quadratic equations

What is the shape of the parent graph of a cubic function?

• A circle

• A straight line

• A parabola

• A cubic curve

In the first example, what are the coordinates of the vertex?

• (-3, 30)

• (2, 5)

• (5, -2)

• (0, 0)

What is the first step in solving for the equation of a cubic graph?

• Graph the function

• Determine the locator point and label it as h, k

• Solve for x

• Find the y-intercept

What is the value of 'a' in the first example after solving?

• -1/16

• 1/16

• -1/8

• 1/8

In the second example, what is the value of 'a' after solving?

• 1/2

• -1/2

• 2

• -2

What is the final equation form for the second example?

• y = 2(x + 1)^3 - 7

• y = -2(x - 1)^3 - 7

• y = 2(x - 1)^3 + 7

• y = -2(x + 1)^3 - 7

In the third example, what is the vertex of the cubic graph?

• (3, 5)

• (7, -2)

• (5, -4)

• (0, 0)

What is the value of 'a' in the third example after solving?

• 1/2

• 1/4

• -1/2

• -1/4

What is the final equation form for the third example?

• y = 1/4(x - 5)^3 - 4

• y = -1/4(x + 5)^3 + 4

• y = 1/4(x + 5)^3 - 4

• y = -1/4(x - 5)^3 + 4