Download Chapter 8.1 Identifying Quadratic Functions.notebook

Chapter 8.1 Identifying Quadratic Functions.notebook
February 14, 2017
Homework Question???
Bellwork
Solve each inequality and graph the solutions.
1) 3 x > 15
2) ­7 < 4x + 3 < 4
3) Let a represent a non­zero rational number and let b represent an irrational number. which expression could represent a rational number?
A. ­b B. a + b
C. ab
D. b2
4) Fill in the table for the function y = x2 + 2
x
y
­2 ­1
0
1
2
Feb 10­7:39 AM
Chapter 8.1 Identifying Quadratic Functions
Feb 13­3:39 PM
Quadratic Function: any function that can be written in the standard form y = ax2 + bx + c, where a, b, and c are real numbers and a ≠ 0. (examples: y = x2, y = 3x2 + 4x ­ 8, y = x2 + 2 ­ 3)
Identify quadratic functions and determine whether they have a minimum or a maximum. Graph a quadratic function and give its domain and range.
y = x2
Feb 10­7:50 AM
Feb 10­7:52 AM
The graph of a quadratic function is a curve called a parabola.
We can identify a Quadratic Function by looking at it's equation, a table or a graph.
1) Identify Quadratic Functions by it's Equation:
We can graph a parabola by graphing enough ordered pairs and connecting the points with a smooth curve.
Use a table of values to graph each quadratic function.
a. x
­2
­1
0
1
2
b. x
­2
­1
0
1
2
Can the function be written in the form y = ax2 + bx + c?
a. y = 7x + 3
c. y + 4x = x2 ­ 6
b. y ­ 10x2 = 9
c. y ­ 3 = ­2x ­ 4
y = ­4x2
Which way do the graphs open? Why do you think they open that way?
Feb 10­7:59 AM
Feb 10­9:01 AM
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Chapter 8.1 Identifying Quadratic Functions.notebook
February 14, 2017
When a quadratic equation is written in the form y = ax2 + bx + c, the value of a determines the direction a parabola opens.
Opens upward when a > 0.
Opens downward when a < 0.
2) Identify whether a Parabola of a quadratic function opens up or down by looking at the equation.
2
2
a. y ­ ¼x = x ­ 3
b. y = 5x ­ 3x
Vertex
Absolute Maximum
y = 0
Absolute Minimum
y = 0
Vertex: The highest or lowest point on a parabola.
Absolute Minimum: If a > 0, the parabola opens upward, and the y­value of the vertex is the minimum value of the function.
Absolute Maximum: If a < 0, the parabola opens downward, and the y­value of the vertex is the maximum value of the function.
Feb 10­9:11 AM
Feb 10­9:15 AM
Finding Domain and Range:
3) Identify the Vertex and the Minimum or Maximum of each parabola.
a.
Unless a specific domain (all possible input values) is given, you may assume the domain of a quadratic function is all real numbers.
b.
You can find the range of a quadratic function by looking at its graph.
y = x2
c.
d.
Feb 10­9:20 AM
Range: • Graph opens up or down?
• Identify Max or Min
• Find Domain and Range.
Feb 10­12:30 PM
4) Find the Domain and Range.
a.
Homework
P. 526­529 #7­21, 27­43 (odds), 53­60 (all)
b.
Feb 10­12:30 PM
Feb 10­9:29 AM
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