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# 6.4 Graphing Polynomials (Relative Max/Min, Zeros)

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### 6.4 Graphing Polynomials (Relative Max/Min, Zeros)

1. 1. 7.2 Graphing Polynomial Functions Relative maximum Relative minimum
2. 2. Making a table to graph Graph the function f(x) = -x3 - 4x2 + 5 The graph will cross the x axis 3 or less times since the degree is 3. x -4 -3 -2 -1 0 1 2 3 4 f(x) 5 -4 -3 2 5 0 -19 -58 -123
3. 3. Making a table to graph Graph the function f(x) = -x3 - 4x2 + 5 The graph x f(x) -4 5 crosses -3 -4 -2 -3 the x axis -1 2 0 5 3 times 1 2 3 4 0 -19 -58 -123
4. 4. Find the area where the function equals zero f(x) = x4 – x3 - 4x2 + 1 Make a table
5. 5. Find the area where the function equals zero f(x) = x4 – x3 - 4x2 + 1 Make a table x f(x) ( -2, 9) ( -1, -1) ( 0, 1) (1, -3) ( 2, -7) ( 3, 19) ( 4, 129)
6. 6. Find the area where the function equals zero f(x) = x4 – x3 - 4x2 + 1 Make a table Where are the x f(x) ( -2, 9) zeros? ( -1, -1) between ( 0, 1) -2 and -1 (1, -3) ( 2, -7) - 1and 0 ( 3, 19) 0 and 1 ( 4, 129) 2 and 3
7. 7. What are the Relative Maximum or Relative Minimum It is an area where the highest or lowest points happen. We make a table. Graph the points and look for the highest and lowest points.
8. 8. What are the Relative Maximum or Relative Minimum Make the table for f(x) = x3 – 4x2 + 5 x f(x) ( -2, -19) (-1, 0) ( 0, 5) ( 1, 2) ( 2, -3) ( 3, -4) ( 4, 5) ( 5, 30)
9. 9. What are the Relative Maximum or Relative Minimum Make the table for f(x) = x3 – 4x2 + 5 x f(x) Relative Max ( -2, -19) near x=0 (-1, 0) ( 0, 5) ( 1, 2) ( 2, -3) ( 3, -4) ( 4, 5) ( 5, 30) Relative Min near x = 3 .
10. 10. Graph the function Between what numbers are the zeros of the function?
11. 11. Graph the function Between what numbers are the zeros of the function? Between -7 and -6 -4 and -3 3 and 4
12. 12. Graph the function Between what numbers are the Relative Max. and Min. of the function? Between -6 and -5 R. Min 0 and 2 R. Max
13. 13. Homework Page 356 # 13 – 25 odd
14. 14. Homework Page 356 # 14 – 26 even