1. February 27, 2012 At the end of today, you will evaluate polynomial functions and identify the general graphs of the functions. Warm-up: With a partner, sketch the graph and describe what they look like. 1.f(x) = -x 2 – 6x + 52. f(x) = x 4 – 3x 2 + 1 3. f(x) = x 3 + 3x 2 – 2 4. f(x) = -x 5 – x 4 + 2x 3 *Finals in 17 school days! *Spring break in 20 school days! HW 7.1: Pg. 350 #16-44even

2. Lesson 7.1 Analyzing Polynomials The degree is of the polynomial is the highest power of the polynomial. f(x) = x 5 + 3x 3 – 2x + 1 Polynomials are always written in power descending order. The leading coefficient is the coefficient with the highest power. Odd degrees – x, x 3, x 5, x 7, etc… Even degrees – x 2, x 4, x 6, etc…

3. For each graph from the warm-up, describe the end behavior, determine whether it is an odd or even degree polynomial, and state the number of zeros. What are some characteristics of even and odd degree polynomials? EvenOdd

4. Polynomial Functions What do you remember about function notation? Example 1: Find p(-2) for p(x) = 2x 3 + 6x 2 – 10x p(-2) = 2(-2) 3 + 6(-2) 2 – 10(-2) p(-2) = 2(-8) + 6(4) + 20 p(-2) = -16 + 24 + 20 p(-2) = 28 Step 1: Substitute -2 for x Step 2: Evaluate using PEMDAS This means the point (-2, 28) is on the graph 2x 3 + 6x 2 – 10x

5. On your own… 1. Find c(-3) for c(x) = 2x 4 – x 3 + 5x 2. The volume of air in the lungs during a 5- second respiratory cycle can be modeled by v(t) = -0.037t 3 + 0.152t 2 + 0.173t, where v is the volume in liters and t is the time in seconds. Find the volume of air in the lungs 2 seconds into the respiratory cycle.

6. What if you evaluate variables in a function? Example 2: If g(x) = 2x 2 – 4x + 3 what is the value for g(3a)? g(3a) = 2(3a) 2 – 4(3a) + 3 g(3a) = 2(9a 2 ) – 12a + 3 g(3a) = 18a 2 – 12a + 3 Step 1: Substitute 3a for x. Step 2: Simplify using PEMDAS

7. Practice makes perfect! If d(x) = 4x 2 – 5x + 2, find each value for the following: 1.d(2a 2 ) 2.d(a + 1) 3.d(1) + d(-2)