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9.5 Solving Quadratic Equations by Graphing Ms. Wu

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Warm-Up

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Objectives Warm-Up (5 min.) Reminder 101 (3 min.) Review (10 min.) Quiz, Evaluation, Folder Organization ( 27 min.) Introduction (5 min.) 9.5 Workshop (20 min.) In-Class Assignment (20 min.)

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Remind 101 – 3rd

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Remind 101 – 4 th

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Review Vertex (2, -1) y-int (0, 3) Axis of Symmetry x = 2 Domain: all real numbers Range: y ≥ -1 Minimum Opens UP Zeros: 1 and 3

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Review For the parent function, y = x 2, what is the transformed function that is ____________? 7 units up: y = x 2 + 7 2 times wider: y = ½x 2 1/3 times narrower and down 1 unit: y = 3x 2 – 1

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Review For the function, y = x 2 +2x-1, what is the ________? Axis of symmetry? x = Vertex: (-1, -2) Does it open up or down? UP Is it a maximum or minimum? MINIMUM y-intercept: (0, -1) Domain: all real numbers Range: y ≥ -1

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Quiz -> Evaluation - > Organization -> Lunch Notes 9.1 9.2 9.3 9.4 Roller Coaster 1 st Blueprint 2 nd Blueprint Homework 9.1 9.2 9.3 9.4 In-Class Assignments 9.2 Exploration (Axis of Symmetry) 9.4 Transformers Exploration Is your folder ready for an organization grade?? Everything must be completed…folders will be picked up for a grade next class period!!

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Announcement Go to Ms. Wu’s website: annwustudentteaching.webs.comannwustudentteaching.webs.com Go to the tab “For Students (3 rd & 7 th )” New Format: Homework: Watch videos, take notes In-Class: Work on assignment, get help, quiz

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Solving Quadratic Equations by Graphing A quadratic function is a function that can be written in the standard form y = ax 2 +bx+c. A quadratic equation is an equation that can be written in the standard form 0 = ax 2 +bx+c. When writing a quadratic function as its related quadratic equation you replace y with 0. Then, you solve the equation by finding its zero(s) or roots or x-int.

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Ms. Wu’s hint: Remember to move everything to one side until you have everything equal to 0! Examples: 1. x 2 -8x-16=2x 2 -x 2 -8x-16 = 0 zero: -4 2. 6x+10=-x 2 x 2 +6x+10=0 zero: none 3. –x 2 +4 = 0 zeros: -2, 2

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Parabolic Solar Ovens Video: Parabolic Solar Ovens in Coast RicaParabolic Solar Ovens Video: How to Cook Food Using Solar OvensHow to Cook Food Using Solar Ovens

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Joseph is trying to build a solar oven in his backyard to cut down on the cost of electricity. He did some research and found that the sun’s rays are best captured by the quadratic function y = x 2 -8x+12. Question: Joseph needs to buy a parabolic mirror at Lowe’s, how wide should the diameter of the mirror be?

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Mirror needs to be 4 feet in diameter.

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In-Class & Homework Complete the evens on 9-5. Turn in by the end of class. Homework: complete notes on how to FOIL and FACTOR. Watch videos online. Organize folder!!

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