3/3/ Week Monday: Review and take quiz on: Simplify in + - * / complex numbers Justification Simplify rational exponents Convert from radical to rational Convert from rational to radical

Tuesday Warm Up Let f(x) = y = x + 2 and g(x) = y = -x + 4 Handed out Volume 2 books Let f(x) = y = x + 2 and g(x) = y = -x + 4 Calculate h(x) = f(x) * g(x) g(x) = -x2 + 2x + 8 Graph all three functions in the calculator Compare and contrast the curves

Tuesday Graph f(x) = y = x + 2 Graph g(x) = y = -x + 4 Calculate h(x) = f(x) * g(x) Plot h(x) What do you notice about f(x), g(x) and h(x): Shape Domain Range x-intercept y-intercept increase/decrease end behavior Rate of change Max/Min

Who let the dogs in, Vol 2 page 858 What do you notice about f(x), g(x) and h(x): Shape Domain Range x-intercept y-intercept increase/decrease end behavior Rate of change Max/Min

HW: Skills page 880 & 881, # 8 – 11 all

Wednesday March 5 Computer Lab half day reviewing rational/irrational numbers Room T-10 Username: Students\lastname last 4 of id Password: whole student id Google Chrome Allow Popups http://carnegielearning.com School ID: salem hs-30013 Login: first initial, last name, last 4 digits of student ID Password McNutt – Salem 34175, Flatshoals 15175

Find the x-intercepts, y-intercepts, local maximums and minimums and intersections

Find the x-intercepts, y-intercepts, local maximums and minimums and intersections

Thursday, March 6 Warm Up: Calculator exercise Letters from home? Factoring Quiz tomorrow over calculator operation To qualify to re-take complex/rational/radical quiz, you need to: Turn in list of exponential rules, with an example of each Correct Radical and Rational Exponent work sheet (graded) and Operations with Complex Numbers work sheet

HW - Factor the given expression, set equal to zero and solve for x: Skills page 895, # 3 & 5 Skills page 896, # 7 & 9, add multiply together to see the quadratic Skills page 905, # 3 & 5, add multiply to see the quadratic

Friday 3/7 Warm Up Find the zeros and vertex of the following factored quadratics using algebra. Multiply the factors together to find the quadratic and graph Describe each graph (vertex, increase/decrease, open up/down, zeros, y-intercept, end conditions) f(x) = (x + 1)(x +3) g(x) = (x + 2)(x – 4) The above form is called the “intercept form”. Why do you think it is called that? The factors and quadratic can be represented by an area model

Basic Steps for Factoring Standard Form if a = 1 Put equation in standard form – make a > 0 Factor out the GCF Determine a, b, and c Find the factors of a times c that add to b If a = 1, the factors are (x + f1)(x + f2) = 0 This is called the “intercept form”, why? Use the zero product rule to find the solutions Verify by substituting solutions into the original equation

Emphasize the “cross” idea and logic: If ac > 0: both factors must be positive or negative. If b > 0, they are both positive If b < 0, they are both negative If ac < 0: One factor is positive and one is negative If b > 0, the larger one is positive If b < 0, the larger one is negative

Product (ac) Factor 1 Factor 2 Sum (b)

Factor Trinomials with a = 1 Factor x2 + 2x – 8 = 0 Factor x2 + 6x = -8 Factor x2 + 12 = -7x Factor x2 - 24x - 81 = 0 Factor 2x3 + 16x2 = -24x Factor 4x3y - 20x2y + 16xy = 0 Factor x2 + 3x - 18 = 0

Basic Steps for Factoring Standard Form if a  1 Put equation in standard form – make a > 0 Factor out the GCF Determine a, b, and c Find the factors of a times c that add to b If a 1, rewrite the equation replacing the b term with the factors found above and factor by grouping Use the zero product rule to find the solutions Verify by substituting solutions into the original equation

Emphasize the “cross” idea and logic: If ac > 0: both factors must be positive or negative. If b > 0, they are both positive If b < 0, they are both negative If ac < 0: One factor is positive and one is negative If b > 0, the larger one is positive If b < 0, the larger one is negative

Solving Polynomial Equations Example: find the zeros of 6x2 + x – 12 = 0 ac = -72 and the factors of -72 are: 2 and -36, 3 and -24, 4 and -18, 6 and -12, 9 and -8, -2 and 36, -3 and 24, -4 and 18, -6 and 12, -9 and 8 The two that add to 1 is 9 and -8, so we replace x with 9x and -8x and factor by grouping.

Product (ac = -72) Factor 2 (-8) Factor 1 (+9) Sum (b = 1)

Continuing: Example: find the zeros of 6x2 + x – 12 = 0 6x2 + 9x – 8x – 12 = 0 3x(2x + 3) – 4(2x + 3) = 0 (2x + 3)(3x – 4) = 0 x = -3/2 or x = 4/3

Summary Find the factors of “ac” that add to “b” If ac > 0: both factors must be positive or negative. If b > 0, they are both positive If b < 0, they are both negative If ac < 0: One factor is positive and one is negative If b > 0, the larger one is positive If b < 0, the larger one is negative

HW Skills page 931 - 935 # 1 – 17 odds