objective: swbat… to graph quadratic function of the form y = ax 2 and y =ax 2 + c

Objective: SWBAT… To graph quadratic function of the form y = ax2 and y =ax2 + c

Bell Ringer:Analyze -16x2 + 64 … explain what it is and classify it.

•5 minutes•4 minutes•3 minutes•2 minutes•1 minute•30 seconds•TIMES UP!!!

Homework: Textbook- Read 546 - 549 Do: P. 549 -552: 1 – 4, 5, 8, 11, 14, 17, 21, 24, 48, 34-35

What are the variables in the playground scenario?

Consider

• quantity of children• Time of day• temperature

There are 6 children playing in a playground . Is the number of children playing a constant or a variable quantity?

The # of children is a variable quantity because it will change.

Objective: SWBAT… To graph quadratic function of the form y = ax2 and y = ax2 + c

Homework: Textbook- Read 546 - 549 Do: P. 549 -552: 1 – 4, 5, 8, 11, 14, 17, 21, 24, 48, 34-35

What other variables might affect the number of children at the playground?

Time of day; temperature…

Independent Variable

Definitions

A variable whose value depends on the value of another variable. It changes in response to another variable. Also called OUTPUTS

Objective: SWBAT… To graph quadratic function of the form y = ax2 and y = ax2 + c

Homework: Textbook- Read 546 - 549 Do: P. 549 -552: 1 – 4, 5, 8, 11, 14, 17, 21, 24, 48, 34-35

Dependent Variable

The variable that changes another variable. Also called INPUTS

Playground

Temperature/Weather

Time of day

# of Children

Definitions

The relationship that pairs each input value with exactly one output variable

Objective: SWBAT… To graph quadratic function of the form y = ax2 and y = ax2 + c

Homework: Textbook- Read 546 - 549 Do: P. 549 -552: 1 – 4, 5, 8, 11, 14, 17, 21, 24, 48, 34-35

Function

Example:y = 3x + 1 Or f(x) = 3x + 1

Note:f(x) or the function of x is read: “F” of “x”

Recall Classification of Polynomials…

Objective: SWBAT… To graph quadratic function of the form y = ax2 and y = ax2 + c

Homework: Textbook- Read 546 - 549 Do: P. 549 -552: 1 – 4, 5, 8, 11, 14, 17, 21, 24, 48, 34-35

Polynomial Degree Name Using Degree # of Terms Name using # of terms

6 0 Constant 1 Monomial

6x + 2 1 Linear 2 Binomial

2x2 + 4x + 2 2 Quadratic 3 Trinomial

21x3 3 Cubic 1 Monomial

5y4 - 3y3 + 2y 4 Fourth Degree 3 Trinomial

Definitions A function that can be written in the form of y = ax2 bx + c , where a≠ 0. This form is called standard form of a quadratic equation

Objective: SWBAT… To graph quadratic function of the form y = ax2 and y = ax2 + c

Homework: Textbook- Read 546 - 549 Do: P. 549 -552: 1 – 4, 5, 8, 11, 14, 17, 21, 24, 48, 34-35

Quadratic Function

Example: y = 3x2 y = x2 + 9 y = x2 -x -2

Note:f(x) or the function of x is read: “F” of “x”

The graph of a quadratic function that is like a U-shaped curve

Parabola

The simplest quadratic function is f(x) = x2 or y = x2. , called the quadratic parent function

Definitions

Objective: SWBAT… To graph quadratic function of the form y = ax2 and y = ax2 + c

Homework: Textbook- Read 546 - 549 Do: P. 549 -552: 1 – 4, 5, 8, 11, 14, 17, 21, 24, 48, 34-35

Axis of symmetry

Vertex

The fold or line that divides the parabola into to matching halves

The highest or lowest point of a parabola, which is the axis is symmetry.

Look at the following quadratic equations:

http://www.mathsisfun.com/data/grapher-equation.html

Lets look at some examples:

1. y = x2 2. y = 2x2

3. y= -2x2

4. y = 10x2

Objective: SWBAT… To graph quadratic function of the form y = ax2 and y = ax2 + c

Homework: Textbook- Read 546 - 549 Do: P. 549 -552: 1 – 4, 5, 8, 11, 14, 17, 21, 24, 48, 34-35

How does the value of “a” affect the vertex of the parabola?

Explain how your knowledge of slope can help you remember how the value of the “a” (from standard form) affects the width of a parabola?

Reflection

Objective: SWBAT… To graph quadratic function of the form y = ax2 and y = ax2 + c

Homework: Textbook- Read 546 - 549 Do: P. 549 -552: 1 – 4, 5, 8, 11, 14, 17, 21, 24, 48, 34-35

Remove everything from your desk except a pen or pencil

QUIZ!!! 5 – 10 minutes

Objective: SWBAT… To graph quadratic function of the form y = ax2 and y = ax2 + c

Homework: Textbook- Read 546 - 549 Do: P. 549 -552: 1 – 4, 5, 8, 11, 14, 17, 21, 24, 48, 34-35