1. 10.1: Quadratic Equations and Functions
Grade Distribution For Test 4-2
3rd
5th
8th A 7 3 6 B 11 8 9 C 10 5 D 2 F 1
No Shows
100+
Range
59-99
51-93
57-99
Avg
81.72
76.43
82.64
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10.1: Quadratic Equations and Functions

2. 10.1: Quadratic Equations and Functions
SECTION 10.1
Labeling Quadratics
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10.1: Quadratic Equations and Functions

3. 10.1: Quadratic Equations and Functions
Intro to Quadratics
Quadratic Function is viewed as, ax2 + bx + c = 0, where a ≠ 0
Parabola is an u–shaped graph
If a is positive, it opens up
If a is negative, it opens down
In a table, the common difference is twice as much as a linear function.
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10.1: Quadratic Equations and Functions

4. 10.1: Quadratic Equations and Functions
4 Corner Model
Take out your Characteristics Notes out
Any function that can be written in the standard form of y = ax2 + bx + c
y = 4x2 – 2x + 3
y = –3x2 – 1
y = (1/2)x2
Parent Function: y = x2
Examples:
Bridges, Falling Objects, Rockets
Quadratics x y –4 8 –1 2 4
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10.1: Quadratic Equations and Functions

5. 10.1: Quadratic Equations and Functions
Quadratic Graph
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10.1: Quadratic Equations and Functions

6. 10.1: Quadratic Equations and Functions
Differences between Linear vs Quadratic
Linear
Quadratic
ALGEBRAIC:
2nd degree
Need to know at least 3 point to write equation.
Range based on max or min y values
ALGEBRAIC:
1st degree
Need to know two points to write equation
Range is all real numbers
ALGEBRAIC:
Both have linear and constant terms
Domain is all real numbers
VERBAL:
Rate of change varies looking for maximum
VERBAL:
Constant Rate of Change
GRAPH:
Line
Slope between any 2 points the same
GRAPH:
Parabola or “u-shaped”
Slope between two point not necessary the same
Has a vertex
TABLE:
2nd differences are equal
TABLE:
1st difference are equal
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10.1: Quadratic Equations and Functions

7. 10.1: Quadratic Equations and Functions
Example 1
Is this graph linear or quadratic?
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10.1: Quadratic Equations and Functions

8. 10.1: Quadratic Equations and Functions
Example 2
Is this graph linear or quadratic?
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10.1: Quadratic Equations and Functions

9. 10.1: Quadratic Equations and Functions
Example 3
Is this equation, –12x + 3y = 9 linear or quadratic?
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10.1: Quadratic Equations and Functions

10. 10.1: Quadratic Equations and Functions
Your Turn
Is this equation, –12x2 + 2y = 6 linear or quadratic?
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10.1: Quadratic Equations and Functions

11. 10.1: Quadratic Equations and Functions
Quadratic Tables
Take the difference from the x and the y’s.
If the x’s are consistent, take the difference of the y’s throughout. If the changes of x-coordinates are not consistent, take the slope.
If the y-coordinates are consistent, it is a LINEAR function
If the y-coordinates are not consistent, take the difference again. If they are consistent for a second time, it is a QUADRATIC function
If they are not consistent again, it can be a cubic function or not a function at all.
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10.1: Quadratic Equations and Functions

12. 10.1: Quadratic Equations and Functions
Example 4
Is this table linear, quadratic, or neither? Show work. x y –2 –7 –1 –5 –3 1 2
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10.1: Quadratic Equations and Functions

13. 10.1: Quadratic Equations and Functions
Example 5
Is this table linear, quadratic, or neither? Show work. x y –2
–14 –1 –6 –4 1 –8 2
–18
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10.1: Quadratic Equations and Functions

14. 10.1: Quadratic Equations and Functions
Example 6
Is this table linear, quadratic, or neither? Show work. x y –2 –6 –1 1 2 3 10
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10.1: Quadratic Equations and Functions

15. 10.1: Quadratic Equations and Functions
Your Turn
Is this table linear, quadratic, or neither? Show work. x y –2 11 –1 6 3 1 2
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10.1: Quadratic Equations and Functions

16. 10.1: Quadratic Equations and Functions
4 Corner Model
Take out your Characteristics Notes out
Vertex: Ordered pair that can be the highest or lowest point on a graph
A vertical line that divides a parabola into two symmetrical values. Typically, it is x = a number
Quadratics
Roots: Where the graph crosses the x-Line
AKA: X-intercepts, Zeros, Solution
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10.1: Quadratic Equations and Functions

17. 10.1: Quadratic Equations and Functions
Definitions
Roots: The solutions to the equation Also known as solutions
X-intercepts: Point(s) where the graph crosses the x–Line. Also known as roots and x-intercepts.
Vertex: Minimum or maximum value
Line of Symmetry: Line that separates the graph in half; always is x equals
Y-intercept: Crosses the y-axis
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10.1: Quadratic Equations and Functions

18. 10.1: Quadratic Equations and Functions
Definitions
Determine:
How it opens: Does it open up or down?
Vertex: The highest/lowest part of the graph
Roots: Where does it cross the x-Line?
Y-Intercept: Where does it cross the y-Line?
Line of Symmetry: Equation of which the X of the vertex
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10.1: Quadratic Equations and Functions

19. 10.1: Quadratic Equations and Functions
Example 7
Given this graph, identify how the graph opens, vertex, roots, y-intercept and line of symmetry.
Opens:
Vertex:
Roots:
Y-intercept:
Line of Symmetry:
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10.1: Quadratic Equations and Functions

20. 10.1: Quadratic Equations and Functions
Example 8
Given this graph, identify how the graph opens, vertex, roots, y-intercept and line of symmetry.
Opens:
Vertex:
Roots:
Y-intercept:
Line of Symmetry:
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10.1: Quadratic Equations and Functions

21. 10.1: Quadratic Equations and Functions
Your Turn
Given this graph, identify how the graph opens, vertex, roots, y-intercept and line of symmetry.
Opens:
Vertex:
Roots:
Y-intercept:
Line of Symmetry:
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10.1: Quadratic Equations and Functions

22. 10.1: Quadratic Equations and Functions
Assignment
Worksheet
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10.1: Quadratic Equations and Functions