Assignment, pencil, red pen, highlighter, textbook, notebook, graphing calculator U4D6 Have out: Bellwork: Write the equation in Vertex form by completing the square then sketch a graph. 2 4 6 8 10 y x –2 –4 –6 –8 –10 +2 + 4 –8 +1 +1 +1 +2 total:

Take out your parent graph toolkit. We are going to add the parent graphs for lines.

PARENT GRAPH TOOLKIT Name: Lines x y x y -3 -2 -1 1 23 x y 10 Name: Lines x y x y -3 -2 -1 1 23 x y 8 Parent Equation: y = x 6 4 Description of Locator: 2 (0, 0) x y–intercept (0, y) –4 –2 2 4 –2 General Equation: –4 y = mx + b –6 –8 Properties: –10 (steepness) Domain: Range: {x| x  R} {y| y  R} b = y–intercept

Now onto something else… Take out today’s worksheet

PG – 56 Using 3 different colors, highlight the equations that seem to be the most alike.

List the similar equations below by category: cubic reciprocal exponential Over the next 3 days, we will study each of these sets of functions. Today we will look at cubic functions. Be sure to have a graphing calculator.

Cubic Locator point (0, 0) Group name: _______________ Functions y = x3 (parent graph) (0, 0) Equation: _____ locator point: _____ 2 4 6 8 10 y x –2 –4 –6 –8 –10 x y –3 –2 –1 1 2 3 –27 Locator point (0, 0) –8 –1 1 8 27 Link to Geo Sketch

Locator point (1, 0) (h, k) y = (x – 1)3 (1, 0) Equation: __________ 2 4 6 8 10 y x –2 –4 –6 –8 –10 x y –2 –1 1 2 3 4 –27 Locator point (1, 0) –8 –1 1 8 27 Link to Geo Sketch

Locator point (2, 1) (h, k) y = (x – 2)3 + 1 (2, 1) Equation: ____________ locator point: _____ 2 4 6 8 10 y x –2 –4 –6 –8 –10 x y –1 1 2 3 4 5 –26 Locator point (2, 1) –7 1 2 9 28 Link to Geo Sketch

Locator point (-2, 0) (h, k) (–2, 0) Equation: ____________ 4 6 8 10 y x –2 –4 –6 –8 –10 x y –5 –4 –3 –2 –1 1 Stretch factor: –13.5 Locator point (-2, 0) –4 –0.5 0.5 4 13.5 Link to Geo Sketch

PARENT GRAPH TOOLKIT Name: Cubics x y x y -2 -1 1 2 -8 8 (2, 8) 10 Name: Cubics x y x y -2 -1 1 2 -8 8 8 (2, 8) Parent Equation: y = x3 6 4 Description of Locator: 2 (1, 1) (0, 0) x inflection point (h, k) –4 –2 2 4 (–1, –1) –2 General Equation: –4 y = a(x – h)3 + k –6 (–2, –8) –8 Properties: –10 flip horizontal shift Domain: Range: y = +/- a(x – h)3 + k {x| x  R} {y| y  R} Wider or narrower vertical shift

Based on the patterns you have observed, graph the next 4 cubics on the worksheet WITHOUT using a graphing calculator. 2 4 6 8 10 y x –2 –4 –6 –8 –10

Finish today's assignment: PG 62-68 & worksheets