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Evaluate the expression when x = – 4

Warm Up #8. Evaluate the expression when x = – 4. 2. – 3 x 3 – 2 x 2 + 10. 1. x 2 + 5 x. (-4) 2 + 5(-4). – 3(-4) 3 – 2(-4) 2 + 10. 16 – 20. 192 – 32 + 10. -4. 170. Check your HW. 1. a. h ( x ) = x 4 – x 2 + 3.

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Evaluate the expression when x = – 4

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  1. Warm Up #8 Evaluate the expression when x=–4 2.–3x3 – 2x2 + 10 1.x2 + 5x (-4)2 + 5(-4) –3(-4)3 – 2(-4)2 + 10 16 – 20 192– 32 + 10 -4 170

  2. Check your HW

  3. 1 a. h (x) = x4 – x2 + 3 b. g (x) = 7x – 3 + πx2 EXAMPLE 1 Identify polynomial functions Decide whether the function is a polynomial function.If so, write it in standard form and state its degree, and leading coefficient. 4 c. f (x) = 5x2 + 3x –1– x d. k (x) = x + 2x– 0.6x5

  4. EXAMPLE 2 Evaluate by direct substitution Use direct substitution to evaluatef (x) = 2x4 – 5x3 –4x + 8whenx = 3. f (x) = 2x4 –5x3 – 4x+ 8 Write original function. f (3) = 2(3)4 – 5(3)3 – 4(3) + 8 Substitute 3 for x. = 162 – 135 – 12 + 8 Evaluate powers and multiply. = 23 Simplify

  5. for Examples 1 and 2 GUIDED PRACTICE Decide whether the function is a polynomial function. If so, write it in standard form and state its degree, type, and leading coefficient. 1. f (x) = 13 – 2x ANSWER polynomial function; f (x) = –2x + 13;degree 1, type: linear, leading coefficient: –2

  6. for Examples 1 and 2 GUIDED PRACTICE 2. p (x) = 9x4 – 5x – 2 + 4 ANSWER not a polynomial function 3. h (x) = 6x2 + π – 3x ANSWER polynomial function; h(x) = 6x2 – 3x + π;degree 2, type: quadratic, leading coefficient: 6

  7. for Examples 1 and 2 GUIDED PRACTICE Use direct substitution to evaluate the polynomial function for the given value of x. 4. f (x) = x4 + 2x3 + 3x2 – 7; x = –2 f (x) = (-2)4 + 2(-2)3 + 3(-2)2 – 7 f (x) = 16 – 16 + 12 – 7 f (x) = 5

  8. Write the coefficients of f (x) in order of descending exponents. Write the value at which f (x) is being evaluated to the left. STEP 1 EXAMPLE 3 Evaluate by synthetic substitution Use synthetic substitution to evaluate f (x) from Example2 when x = 3. f (x) = 2x4 – 5x3 –4x + 8

  9. for Examples 3 and 4 GUIDED PRACTICE Use synthetic substitution to evaluate the polynomial function for the given value of x. 6. f(x) = 5x3 + 3x2–x + 7; x = 2

  10. for Examples 3 and 4 GUIDED PRACTICE Use synthetic substitution to evaluate the polynomial function for the given value of x. 7. g (x) = –2x4–x3 + 4x – 5; x = –1

  11. Graphing Polynomial Functions

  12. Polynomial End Behavior Even Functions Even Functions Positive Leading Coefficient Even Functions Negative Leading Coefficient

  13. Polynomial End Behavior Odd Functions Odd Functions Positive Leading Coefficient Odd Functions Negative Leading Coefficient

  14. ANSWER The correct answer is D. EXAMPLE 4 Standardized Test Practice

  15. 8. Describe the degree and leading coefficient of the polynomial function whose graph is shown. ANSWER degree: odd, leading coefficient: negative for Examples 3 and 4 GUIDED PRACTICE

  16. To graph the function, make a table of values and plot the corresponding points. Connect the points with a smooth curve and check the end behavior. a. EXAMPLE 5 Graph polynomial functions Graph (a)f (x) = –x3 + x2 + 3x – 3

  17. for Examples 5 and 6 GUIDED PRACTICE Graph the polynomial function. 9. f(x) = x4 – 6x2 + 3 x f(x) -3 30 -2 -5 -1 -2 0 3 1 -2 2 -5 3 30

  18. Classwork/Homework 5.2 Worksheet 5.2 1-15 all

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