Sketching Graphs of Polynomials

Even Degree
- Leading Coeff. Even Degree
+ Leading Coeff. Odd Degree
- Leading Coeff. Odd Degree
+ Leading Coeff.

• Even Degree
  - Leading Coeff.

• Even Degree
  + Leading Coeff.

• Odd Degree
  - Leading Coeff.

• Odd Degree
  + Leading Coeff.

What is true of the following polynomial:

• It's graph is a downward facing parabola

• It has no real solutions

• It will bounce off the x-axis and -2 and 3

• It will cross the x-axis and -2 and 3

What is the y-intercept?

• (0, -24)

• (-1, 0)

• (0, 18)

• (0, 0)

What is the end behavior?

• down-up

• up-down

• up-up

• down-down

• The function has an Odd degree
• The function has an Even degree
• The function has 5 real zeros
• The function has a Positive coefficient

• The function has an Even degree
• The function has a Negative coefficient
• The function has an Odd degree
• The function has 3 real zeros

• (-2.55, 0), (2.55, 0)
• (-3, 0), (-2, 0), (2, 0), (3, 0)
• (0, 36)
• (0, -3), (0, -2), (0, 2), (0, 3)

What is the end behavior of the following polynomial?

y = 3(x + 4)²(x + 1)(x - 3)²?

• falls to the right and left

• rises to the right and left

• falls to the left and rises to the right

• falls to the right and rises to the left

Odd Multiplicities have which of the following effects on the x-axis?

• Cross the x-axis

• Turn on the x-axis

Even Degree
- Leading Coeff. Even Degree
+ Leading Coeff. Odd Degree
- Leading Coeff. Odd Degree
+ Leading Coeff.

• Even Degree
  - Leading Coeff.

• Even Degree
  + Leading Coeff.

• Odd Degree
  - Leading Coeff.

• Odd Degree
  + Leading Coeff.