objective: swbat… to graph quadratic function of the form y = ax 2 and y =ax 2 + c
DESCRIPTION
Homework: Textbook- Read 546 - 549 Do: P. 549 -552: 1 – 4, 5, 8, 11, 14, 17, 21, 24, 48, 34-35. Objective: SWBAT… To graph quadratic function of the form y = ax 2 and y =ax 2 + c. Bell Ringer: Analyze -16x 2 + 64 … explain what it is and classify it. 5 minutes 4 minutes - PowerPoint PPT PresentationTRANSCRIPT
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