3.7 Investigating Graphs of Polynomial Functions

List the local maxima and minima of the following function:
 $2x^4-x^3-2x^2-12$  
Put answers in the following form:
Max:  $\left(x_1,y_1\right),\ \left(x_2,y_2\right)$ , Min:  $\left(x_1,y_1\right),\ \left(x_2,y_2\right)$  

The end behavior of a polynomial function is determined by the degree and the sign of the leading coefficient.
Identify the degree of the polynomial and the sign of the leading coefficient 

• Leading Coefficient Positive
  Degree - Even
• Leading Coefficient Positive
  Degree - Odd
• Leading Coefficient Negative
  Degree - Even
• Leading Coefficient Negative
  Degree - Odd

Tags

CCSS.HSF.IF.B.4

CCSS.HSF.IF.C.7

The end behavior of a polynomial function is determined by the degree and the sign of the leading coefficient.
Identify the degree of the polynomial and the sign of the leading coefficient 

• Leading Coefficient Positive
  Degree - Even
• Leading Coefficient Positive
  Degree - Odd
• Leading Coefficient Negative
  Degree - Even
• Leading Coefficient Negative
  Degree - Odd

Tags

CCSS.HSF.IF.B.4

CCSS.HSF.IF.C.7

To determine if the degree of a function is even or odd, look at the...

• x-values

• y-values

• Maximum/ Minimum

• End behaviors

Tags

CCSS.HSF.BF.B.3

The blue dot on this graph represents a(n)...

• Absolute Maximum

• Absolute Minimum

• Local Maximum

• Local Minimum

Tags

CCSS.HSF.IF.B.4

CCSS.HSF.IF.C.7

• (1, 4)
• (0, 2)
• (-1, 0)
• (2, 0)

• (0, 4)
• (2, 0)
• (0, 2)
• (-1, 0)

Tags

CCSS.HSA.REI.D.10

Which function has this end behavior?

• -x²-3x+1
• -x³+2x²+3
• x⁴+3x³-4x+1
• x⁵-4x⁴+2x²-1

Tags

CCSS.HSF.IF.B.4

CCSS.HSF.IF.C.7

Which function has this end behavior?

• -1x⁴-3x³+3
• -2x⁷+2x⁴+4
• 3x⁸+3x⁵-4x+7
• 4x⁵-4x⁴+2x³-9

Tags

CCSS.HSA.APR.A.1

Which function has this end behavior?

• -1x⁴-3x³+3
• -2x⁷+2x⁴+4
• 3x⁸+3x⁵-4x+7
• 4x⁵-4x⁴+2x³-9

Tags

CCSS.HSA.CED.A.2

CCSS.HSA.REI.D.10