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Starter Duane has a job counting bacteria in water samples In 12 ml he counted 634 bacteria In 18 ml he counted 864 bacteria Write the equation for a linear model How many bacteria in 20 ml How many ml to get 1000 bacteria

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Algebra II Chapter 2 Section 5 When it positively absolutely has to be an absolute value

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Absolute value Everything inside the | | brackets has to be + Treat them like ( ) Do everything inside first… then make + then do everything outside

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F(x) = | x | When x > 0 looks like f(x) = x When x < 0 looks like f(x) = -x When x = 0 is called the vertex

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f(x) = |mx + b| + c Find the vertex with ( -b / m, c) To the right of the vertex graph y = mx + b + c To the left of the vertex graph y = -(mx + b) + c

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Make a table Find the vertex using ( -b/m, c) Select 3 values to the left and 3 values to the right of the vertex Make a table of values Graph both the ordered pairs Connect the dots, it should make a V

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Up or down |mx + b| V is normal -|mx+b| V is upside down

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Linear equations Isolate |mx + b | Separate into mx + b >0, -(mx + b) < 0 Graph each equation over the appropriate domain

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Graph y = |x-3| + 5 y = |x-3| + 5 y - 5 = |x-3| Where x - 3 > 0 y - 5 = (x-3) y - 5 = -(x-3) y - 5 = x - 3 y - 5 = -x + 3 y = x + 2 y = -x + 8

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Do Now Page 88 Problems 1-9 odd Problems 19 – 49 odd

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3.9 Graphs of Quadratic Inequalities p. 96-101. Forms of Quadratic Inequalities yax 2 +bx+c y≤ax 2 +bx+cy≥ax 2 +bx+c Graphs will look like.

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