Assignment pencil red pen highlighter textbook GP notebook
Assignment, pencil, red pen, highlighter, textbook, GP notebook, calculator Solve for x. Use “completing the square” to solve #2 and #3. 1) 2) x 2 – 8 x + 1 = 10 +1 +1 +2 total: 3) x 2 + 10 x – 2 = 1
2) x 2 – 8 x + 1 = 10 – 1 +1 2 + 16 x – 8 x + 16 = 9 (x – 4)2 = 25 +1 3) x 2 + 10 x – 2 = 1 +2 +2 x 2 + 10 x + 25 = 3 + 25 +1 (x + 5)2 = 28 x– 4=± 5 +4 +4 x = 4 ± 5 +1 x = – 1, 9 – 5 +2 – 5 +1 +1 +2 total:
Earlier we grouped the following equations: cubic reciprocal exponential Today we will look at exponential functions. Be sure to have a graphing calculator.
Group name: ________ Functions Equation: _____ (parent graph) (0, 1) locator point: _____ x -4 -3 y 0. 063 Locator point (0, 1) 0. 13 -2 0. 25 4 0. 5 1 2 4 8 16 2 -1 0 1 2 3 4 10 y 8 6 – 10 – 8 – 6 – 4 – 2 2 4 6 8 10 x y=0 – 2 – 4 – 6 – 8 – 10 Link to Geo Sketch
(h, k + 1) (0, – 3) locator point: _____ Equation: ____ x -4 -3 y -3. 94 -3. 88 -2 -3. 75 Locator point 4 -3. 5 -3 -2 0 4 12 2 -1 0 1 2 3 4 10 y 8 6 (0, – 3) – 10 – 8 – 6 – 4 – 2 2 – 2 4 6 8 10 x y = – 4 – 6 – 8 – 10 Link to Geo Sketch
(h, k + 1) (– 3, 1) locator point: _____ Equation: ____ x -5 -4 y 0. 25 0. 5 -3 1 -2 -1 0 1 2 3 2 4 8 16 32 64 10 8 Locator point (-3 1) 6 4 y The locator is not the y– intercept. It is always the point that is 1 unit above the asymptote. 2 – 10 – 8 – 6 – 4 – 2 2 4 6 8 10 x y=0 – 2 – 4 – 6 – 8 – 10 Link to Geo Sketch
(h, k + 1) (4, – 2) locator point: _____ Equation: ____ x -1 0 y -2. 97 -2. 94 1 -2. 88 2 3 4 5 6 7 -2. 75 -2 -1 1 5 y The locator 10 is the point that is 1 unit above the 8 asymptote. What is the point? 6 Locator point 4 (4, – 2) 2 – 10 – 8 – 6 – 4 – 2 2 – 2 4 6 8 10 x y = – 3 – 4 – 6 – 8 – 10 Link to Geo Sketch
PARENT GRAPH TOOLKIT x Name: Exponential horizontal shift vertical shift y=k Horizontal asymptote (3, 8) 8 6 -2 Description of Locator: Point that is 1 unit above the (h, k + 1) asymptote General Equation: Properties: y = a b(x – h) + k y -3 Parent Equation: y = 2 x y = a b(x – h) + k 10 y (2, 4) (1, 2) 2 x (0, 1) 4 -1 0 1 1 2 2 4 – 4 3 8 – 6 y=0 – 4 – 2 2 – 8 – 10 Domain: Range: {x| x R} {y| k < y < } 4
Based on the patterns you have observed, graph the next 4 reciprocal functions on the worksheet WITHOUT using a graphing calculator. 10 y 8 6 4 2 – 10 – 8 – 6 – 4 – 2 2 – 4 – 6 – 8 – 10 4 6 8 10 x
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