Objective: Connect transformations of parabolas with their equations in graphing form.  HW Check/Correct in RED  “The Same But Different” Packet (in place of Lessons & 4.1.2)  Notes: Graphing Form Homework: Problems 4-5 to 4-7, 19-20, 23 Day 46: April 13 th

You will be able to easily sketch graphs similar to the following by just looking at the equations: By the End of the Chapter…

y=ax 2 The higher the number you multiply by, the steeper the parabola. The lower the number you multiply by, the wider the parabola. What we know about transforming y=x 2

Vertical CompressionVertical Stretch Transform! Vertical Dilations

Objective: Connect transformations of parabolas with their equations in graphing form. THEN Graph quadratic equations without making tables.  HW Check/Correct in RED  Notes: Graphing Form  Problems 4-34 to  Closure: Graphing Forms Packet Homework: Problems 4-26 to 4-29, 31, 33 Day 47: April 14 th

y = a(x – h) 2 + k ( h, k ): The Vertex The value of a opposite same Positive: Opens UpIf it Increases: Vertical Stretch Negative: Opens DownIf it Decreases: Vertical Compression Graphing Form for a Parabola

Parent Graph: y = x 2 Factored Form: y = __( __x ± __ )( __x ± __) Standard form: y = ax 2 + bx + c Graphing Form: y = a(x – h) 2 + k Same “a” Different Forms for a Quadratic

Same a! Graphing Form to Standard Form

Objective: Graph quadratic equations without making tables. Also, rewrite quadratic equations from standard form into graphing form.  HW Check/Correct in RED  Problems 4-35 to 4-38  Closure: Graphing Forms Packet Homework: “Chapter 4 Homework #1” Worksheet Day 48: April 15 th

Find the vertex Find the stretch factor Use the stretch factor to translate the “first points” Draw the Parabola Example Plot : y = 2(x+3) 2 – 5 2 –3 – 5

Objective: Graph quadratic equations without making tables. Also, rewrite quadratic equations from standard form into graphing form. THEN Learn how to write quadratic equations for situations using the graphing form of the parabola y=a(x-h) 2 +k. Specifically, develop an algebraic strategy for finding the value of the stretch factor, a.  HW Check/Correct in RED & Complete Warm-Up (Handout)  Review Chapter 3 Individual Test  Finish Problems 4-38  Graphing Forms Packet – Fill-in Parabola  Problems 4-46 to 4-49 Homework: Problems 4-40 to 4-44 Parabolas Quiz Wednesday Day 49: April 18 th

Objective: Learn how to write quadratic equations for situations using the graphing form of the parabola y=a(x-h) 2 +k. Specifically, develop an algebraic strategy for finding the value of the stretch factor, a.  HW Check/Correct in RED & Complete Warm-Up (Handout)  Problems 4-46 to 4-49 Homework: “Chapter 4 Homework #2” Handout #1-9 Parabolas Quiz Tomorrow – No Graphing Calculators! Day 50: April 19 th

Warm-Up: 4/18 Consider the graph y = -2(x – 4) Make ONE change in the equation of y so that the graph: a)Opens up. b)Is wider (vertical compression). c)Has one x-intercept. d)Is moved to the left.

Standard Form to Graphing Form Use an algebraic method to write in graphing form Find the value of a: 2. Find the x-intercepts 3. Average the x-intercepts for h 4. Substitute h into the rule for k 5. Substitute a, h, k into the graphing form WARNING:This method does not work if there are no x-intercepts

Standard Form to Graphing Form Use an algebraic method to write in graphing form Find the value of a: 2. Find the x-intercepts WARNING:This method does not work if there are no x-intercepts 3. Average the x-intercepts for h 4. Substitute h into the rule for k 5. Substitute a, h, k into the graphing form

Finding the Equation of a Line Find the equation of a line that passes through the point (3,5) and has a slope of 2. 2 (3,5) (x,y)

Finding a Quadratic Equation with the Vertex and Another Point A rabbit jumped over a 3ft-high fence. The highest point the rabbit reached was 3 feet and it landed 8 feet from where it jumped. Assume the rabbit follows a parabolic path. Sketch a graph and find the equation for the height of the rabbit verses the horizontal distance it has traveled. Label all the known points (8,0) (4,3) (0,0) Include (0,0)! Plug in the vertex Sketch: Substitute into y=a(x-h) 2 +k: Plug in another point Solve for a Since we know the vertex Equation: Plug in a,h,&k

Objective: Assess the first section of Chapter 4 in an individual setting.  HW Check/Correct in RED & Complete Warm-Up (Handout)  Chapter 4 Individual Quiz #1 – No Calculators!  Graphing Forms Packet: Fill-in Cubic and Square Root Homework: Problems 4-55 to 4-58 Day 51: April 20 th

Warm-Up: 4/20 Consider the graph y = -2(x – 4) Make ONE change in the equation of y so that the graph: a)Opens up. b)Is wider (vertical compression). c)Has one x-intercept. d)Is moved to the left. Graph the original equation without using your calculator.

Objective: Transform the graphs of y=x 3 and y=√x.  HW Check/Correct in RED & Find an exponential equation that passes through the points (3, -192) and (6, -12,288).  Graphing Forms Worksheet: Transform – Cubic  Graphing Forms Worksheet: Transform – Square Root Homework: Problems 4-71, 72, 75, 76 Do #1-3 on Square Root Packet Day 52: April 21 st

Objective: Transform the graphs of y=√x and continue to practice graphing quadratics from graphing form.  HW Check/Correct in RED & Complete Warm-Up  Finish Graphing Forms Worksheet: Transform – Square Root  “Graphing Quadratic Functions” Practice Packet Homework: Chapter 4 Homework #4 Worksheet Day 53: April 22 nd

Objective: Transform the graphs of y=√x and continue to practice graphing quadratics from graphing form.  HW Check/Correct in RED & Complete Warm-Up  “Graphing Quadratic Functions” Practice Packet Homework: Problems 4- Day 54: April 25 th