Understanding Polynomial Intercepts

The video tutorial explains how to find the X and Y intercepts of a polynomial function, specifically f(x) = -x^3 + 16. It covers the process of setting the function equal to zero to find the X intercepts and setting X to zero to find the Y intercept. The tutorial also demonstrates using a graphing calculator to verify these intercepts, providing both exact and decimal approximations. The video concludes with a brief mention of complex zeros, which will be addressed in another video.

What is the polynomial function given in the video?

• f(x) = -x^2 + 16

• f(x) = x^2 - 16

• f(x) = -x^3 + 16

• f(x) = x^3 + 16

What is the first step in finding the x-intercepts of a polynomial function?

• Set x = 0

• Set y = 0

• Set f(x) = 1

• Set y = 1

How do you isolate the variable term when solving for x-intercepts?

• Subtract x^3 from both sides

• Add x^3 to both sides

• Multiply both sides by x

• Divide both sides by x

What is the exact value of the x-intercept in terms of cube roots?

• 2 + cube root of 2

• 2 * cube root of 2

• 2 - cube root of 2

• cube root of 16

What is the y-intercept of the polynomial function?

• (16, 0)

• (0, 16)

• (0, 0)

• (0, -16)

What is the purpose of setting x to 0 when finding the y-intercept?

• To find the x-intercept

• To find the y-intercept

• To find the slope

• To find the vertex

What is the approximate decimal value of the x-intercept?

• 3.52

• 3.16

• 2.52

• 2.16

Why might the y-intercept not be visible in the standard graphing window?

• The graph is not centered

• The y-intercept is too large

• The x-intercept is too small

• The y-intercept is negative

What tool is used to verify the intercepts in the video?

• A protractor

• A graphing calculator

• A calculator

• A ruler

What is the final step to verify the y-intercept using the graphing calculator?

• Check the graph

• Check the zoom settings

• Check the table of values

• Check the equation