9.5 Solving Quadratic Equations by GraphingMs. Wu

Warm-Up

• Place a sticky note on any three posters…• RED – need most help• YELLOW – need some help• GREEN – good to go!

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.)

Remind 101 – 3rd

Remind 101 – 4th

Review Vertex (2, -1)

y-int (0, 3)

Axis of Symmetry x = 2Domain: all real numbers

Range: y ≥ -1

Minimum

Opens UP

Zeros: 1 and 3

Review

For the parent function, y = x2, what is the transformed function that is ____________?

• 7 units up: y = x2 + 7• 2 times wider: y = ½x2 • 1/3 times narrower and down 1 unit: y = 3x2 – 1

Review

For the function, y = x2+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

Quiz -> Evaluation - > Organization -> Lunch

• Notes• 9.1• 9.2• 9.3• 9.4

• Roller Coaster• 1st Blueprint• 2nd 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!!

Announcement

• Go to Ms. Wu’s website: annwustudentteaching.webs.com• Go to the tab “For Students (3rd & 7th)”

• New Format:• Homework: Watch videos, take notes• In-Class: Work on assignment, get help, quiz

Solving Quadratic Equations by Graphing

• A quadratic function is a function that can be written in the standard form y = ax2+bx+c.

• A quadratic equation is an equation that can be written in the standard form 0 = ax2+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.

Ms. Wu’s hint: Remember to move everything to one side until you have everything equal to 0!• Examples:• 1. x2-8x-16=2x2 -x2-8x-16 = 0 zero: -4

• 2. 6x+10=-x2 x2+6x+10=0 zero: none

• 3. –x2+4 = 0 zeros: -2, 2

Parabolic Solar Ovens

• Video: Parabolic Solar Ovens in Coast Rica• Video: How to Cook Food Using Solar Ovens

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 = x2 -8x+12.

Question: Joseph needs to buy a parabolic mirror at Lowe’s, how wide should the diameter of the mirror be?

Mirror needs to be 4 feet in diameter.

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!!