Understanding Polynomial Intercepts

The video tutorial explains how to find the vertical and horizontal intercepts of a polynomial function c(t). It begins by defining intercepts and their significance. The vertical intercept is found by setting the input variable t to zero, resulting in the origin as the intercept. For horizontal intercepts, the function c(t) is set to zero, and the equation is solved by factoring, yielding intercepts at t=0, t=2, and t=3. The tutorial concludes with a graphical verification of these intercepts, confirming the calculations.

What is the purpose of setting the function value to zero when finding horizontal intercepts?

• To identify the vertical intercept

• To calculate the slope of the function

• To determine where the graph crosses the horizontal axis

• To find the maximum value of the function

How do you find the vertical intercept of a function?

• Set the output variable to zero

• Set the input variable to zero

• Find the derivative of the function

• Solve for the maximum value

What is the vertical intercept of the function c(t) given in the video?

• (0, 0)

• (1, 0)

• (0, 1)

• (2, 0)

What equation is used to find the horizontal intercepts of c(t)?

• c(t) = -1

• c(t) = 0

• c(t) = 2

• c(t) = 1

What is the first step in factoring the polynomial equation to find horizontal intercepts?

• Multiply all terms by zero

• Add all coefficients

• Factor out the greatest common factor

• Divide by the highest power of t

Which of the following is a horizontal intercept of the function c(t)?

• (4, 0)

• (5, 0)

• (1, 0)

• (2, 0)

What are the factors of the trinomial t^2 - 5t + 6?

• (t - 1)(t - 6)

• (t - 2)(t - 3)

• (t + 2)(t + 3)

• (t - 3)(t + 2)

How many horizontal intercepts does the function c(t) have?

• One

• Two

• Three

• Four

Why is the origin both a vertical and horizontal intercept for the function c(t)?

• Because the function is quadratic

• Because the function has no intercepts

• Because the function is linear

• Because the function passes through the origin

What does the graphical representation of c(t) confirm about the intercepts?

• The function passes through the origin and has other horizontal intercepts

• The function only has horizontal intercepts

• The function only has vertical intercepts

• The function has no intercepts