Lesson: Objectives: 5.1 Solving Quadratic Equations - Graphing DESCRIBE the Elements of the GRAPH...
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Transcript of Lesson: Objectives: 5.1 Solving Quadratic Equations - Graphing DESCRIBE the Elements of the GRAPH...
![Page 1: Lesson: Objectives: 5.1 Solving Quadratic Equations - Graphing DESCRIBE the Elements of the GRAPH of a Quadratic Equation DETERMINE a Standard Approach.](https://reader036.fdocuments.in/reader036/viewer/2022081514/5a4d1b967f8b9ab0599c396b/html5/thumbnails/1.jpg)
Lesson:
Objectives:
5.1 Solving Quadratic Equations - Graphing
DESCRIBE the Elements of the GRAPH of a Quadratic Equation
DETERMINE a Standard Approach to GRAPHING A Quadratic Equation
Use a GRAPHING CALCULATOR to Graph a Quadratic Equation
SOLVE a Quadratic Equation using GRAPHING
![Page 2: Lesson: Objectives: 5.1 Solving Quadratic Equations - Graphing DESCRIBE the Elements of the GRAPH of a Quadratic Equation DETERMINE a Standard Approach.](https://reader036.fdocuments.in/reader036/viewer/2022081514/5a4d1b967f8b9ab0599c396b/html5/thumbnails/2.jpg)
ALGEBRA II 5.1-5.2
TERMS Related to QUADRATIC Functions
![Page 3: Lesson: Objectives: 5.1 Solving Quadratic Equations - Graphing DESCRIBE the Elements of the GRAPH of a Quadratic Equation DETERMINE a Standard Approach.](https://reader036.fdocuments.in/reader036/viewer/2022081514/5a4d1b967f8b9ab0599c396b/html5/thumbnails/3.jpg)
ALGEBRA II 5.1-5.2
TERMS Related to QUADRATIC Functions
QUADRATIC FUNCTION
A FUNCTION described by an EQUATION that can be written in the form:
f(x) = ax2 + bx + c
where a 0
![Page 4: Lesson: Objectives: 5.1 Solving Quadratic Equations - Graphing DESCRIBE the Elements of the GRAPH of a Quadratic Equation DETERMINE a Standard Approach.](https://reader036.fdocuments.in/reader036/viewer/2022081514/5a4d1b967f8b9ab0599c396b/html5/thumbnails/4.jpg)
ALGEBRA II 5.1-5.2
TERMS Related to QUADRATIC Functions
f(x) = ax2 + bx + c
ax2 is the QUADRATIC Term
bx is the LINEAR Term
c is the CONSTANT Term
![Page 5: Lesson: Objectives: 5.1 Solving Quadratic Equations - Graphing DESCRIBE the Elements of the GRAPH of a Quadratic Equation DETERMINE a Standard Approach.](https://reader036.fdocuments.in/reader036/viewer/2022081514/5a4d1b967f8b9ab0599c396b/html5/thumbnails/5.jpg)
ALGEBRA II 5.1-5.2
The GRAPH of a QUADRATIC Function is a
PARABOLA
![Page 6: Lesson: Objectives: 5.1 Solving Quadratic Equations - Graphing DESCRIBE the Elements of the GRAPH of a Quadratic Equation DETERMINE a Standard Approach.](https://reader036.fdocuments.in/reader036/viewer/2022081514/5a4d1b967f8b9ab0599c396b/html5/thumbnails/6.jpg)
ALGEBRA II
ALGEBRA II 5.1-5.2
The GRAPH of a QUADRATIC Function is a
PARABOLA
-14
-12
-8
-6
-4
-20
2
4
-8 -6 -4 -2 2x
f(x) = x² +6x - 4
![Page 7: Lesson: Objectives: 5.1 Solving Quadratic Equations - Graphing DESCRIBE the Elements of the GRAPH of a Quadratic Equation DETERMINE a Standard Approach.](https://reader036.fdocuments.in/reader036/viewer/2022081514/5a4d1b967f8b9ab0599c396b/html5/thumbnails/7.jpg)
ALGE ALGEBRA II 5.1-5.2
-14
-12
-8
-6
-4
-20
2
4
-8 -6 -4 -2 2x
f(x) = x² +6x - 4
AXIS ofSYMMETRY x = - 3
The AXIS of SYMMETRY splits the PARABOLA evenly
NAME the AXIS of SYMMETRY by the Equation of the Line
![Page 8: Lesson: Objectives: 5.1 Solving Quadratic Equations - Graphing DESCRIBE the Elements of the GRAPH of a Quadratic Equation DETERMINE a Standard Approach.](https://reader036.fdocuments.in/reader036/viewer/2022081514/5a4d1b967f8b9ab0599c396b/html5/thumbnails/8.jpg)
ALGEBRA II
-14
-12
-8
-6
-4
-20
2
4
-8 -6 -4 -2 2x
f(x) = x² +6x - 4
AXIS ofSYMMETRY x = - 3
The AXIS of SYMMETRY splits the PARABOLA evenly
NAME the AXIS of SYMMETRY by the Equation of the Line
![Page 9: Lesson: Objectives: 5.1 Solving Quadratic Equations - Graphing DESCRIBE the Elements of the GRAPH of a Quadratic Equation DETERMINE a Standard Approach.](https://reader036.fdocuments.in/reader036/viewer/2022081514/5a4d1b967f8b9ab0599c396b/html5/thumbnails/9.jpg)
ALGEBRA II
-14
-12
-8
-6
-4
-20
2
4
-8 -6 -4 -2 2x
f(x) = x² +6x - 4
AXIS ofSYMMETRY x = - 3
VERTEX (- 3, -13)
The VERTEX is the INTERSECTION of the AXIS of SYMMETRY and the PARABOLA.
NAME the VERTEX by its (x, y) Coordinates.
![Page 10: Lesson: Objectives: 5.1 Solving Quadratic Equations - Graphing DESCRIBE the Elements of the GRAPH of a Quadratic Equation DETERMINE a Standard Approach.](https://reader036.fdocuments.in/reader036/viewer/2022081514/5a4d1b967f8b9ab0599c396b/html5/thumbnails/10.jpg)
ALGEBRA II
QUADRATIC FUNCTION
A FUNCTION described by an EQUATION that can be written in the form:
f(x) = ax2 + bx + c
![Page 11: Lesson: Objectives: 5.1 Solving Quadratic Equations - Graphing DESCRIBE the Elements of the GRAPH of a Quadratic Equation DETERMINE a Standard Approach.](https://reader036.fdocuments.in/reader036/viewer/2022081514/5a4d1b967f8b9ab0599c396b/html5/thumbnails/11.jpg)
ALGEBRA II
QUADRATIC FUNCTION
A FUNCTION described by an EQUATION that can be written in the form:
f(x) = ax2 + bx + c
QUADRATIC EQUATION
A Quadratic Function SET TO ZERO.
0 = ax2 + bx + c
![Page 12: Lesson: Objectives: 5.1 Solving Quadratic Equations - Graphing DESCRIBE the Elements of the GRAPH of a Quadratic Equation DETERMINE a Standard Approach.](https://reader036.fdocuments.in/reader036/viewer/2022081514/5a4d1b967f8b9ab0599c396b/html5/thumbnails/12.jpg)
QUADRATIC EQUATION
A Quadratic Function SET TO ZERO.
0 = ax2 + bx + c
The ROOTS or SOLUTIONS of a Quadratic Equation are the VALUES that make the EQUATION True.
![Page 13: Lesson: Objectives: 5.1 Solving Quadratic Equations - Graphing DESCRIBE the Elements of the GRAPH of a Quadratic Equation DETERMINE a Standard Approach.](https://reader036.fdocuments.in/reader036/viewer/2022081514/5a4d1b967f8b9ab0599c396b/html5/thumbnails/13.jpg)
ALGEBRA II
QUADRATIC EQUATION
A Quadratic Function SET TO ZERO.
0 = ax2 + bx + c
The ROOTS or SOLUTIONS of a Quadratic Equation are the VALUES that make the EQUATION True.
Chapter 6 is all about the DIFFERENT METHODS of
FINDING THE ROOTS
![Page 14: Lesson: Objectives: 5.1 Solving Quadratic Equations - Graphing DESCRIBE the Elements of the GRAPH of a Quadratic Equation DETERMINE a Standard Approach.](https://reader036.fdocuments.in/reader036/viewer/2022081514/5a4d1b967f8b9ab0599c396b/html5/thumbnails/14.jpg)
ALGEBRA II
-10
0
10
20
30
-4 -2 2 4 6 8 10x
x2 – 3x – 10
(1.5, -12.25)
x = 1.5( -2, 0)
( 5, 0)
![Page 15: Lesson: Objectives: 5.1 Solving Quadratic Equations - Graphing DESCRIBE the Elements of the GRAPH of a Quadratic Equation DETERMINE a Standard Approach.](https://reader036.fdocuments.in/reader036/viewer/2022081514/5a4d1b967f8b9ab0599c396b/html5/thumbnails/15.jpg)
How to GRAPH a QUADRATIC FUNCTION:
1. Get the Quadratic Function in EQUATION form.
2. Find the VERTEX X Coordinate
3. Make a table of 5 X points, with the 3rd Point being the VERTEX.
4. Find the Y Coordinate for each X Point
5. CONNECT the Points.
ba2
![Page 16: Lesson: Objectives: 5.1 Solving Quadratic Equations - Graphing DESCRIBE the Elements of the GRAPH of a Quadratic Equation DETERMINE a Standard Approach.](https://reader036.fdocuments.in/reader036/viewer/2022081514/5a4d1b967f8b9ab0599c396b/html5/thumbnails/16.jpg)
x2 + 5x + 6 How to GRAPH a QUADRATIC FUNCTION:
1. Get the Quadratic Function in EQUATION form.
2. Find the VERTEX X Coordinate
3. Make a table of 5 X points, with the 3rd Point being the VERTEX.
4. Find the Y Coordinate for each X Point
5. CONNECT the Points.
ba2
![Page 17: Lesson: Objectives: 5.1 Solving Quadratic Equations - Graphing DESCRIBE the Elements of the GRAPH of a Quadratic Equation DETERMINE a Standard Approach.](https://reader036.fdocuments.in/reader036/viewer/2022081514/5a4d1b967f8b9ab0599c396b/html5/thumbnails/17.jpg)
How to GRAPH a QUADRATIC FUNCTION:
1. Get the Quadratic Function in EQUATION form.
2. Find the VERTEX X Coordinate
3. Make a table of 5 X points, with the 3rd Point being the VERTEX.
4. Find the Y Coordinate for each X Point
5. CONNECT the Points.
ba2
x2 – 8x + 12
![Page 18: Lesson: Objectives: 5.1 Solving Quadratic Equations - Graphing DESCRIBE the Elements of the GRAPH of a Quadratic Equation DETERMINE a Standard Approach.](https://reader036.fdocuments.in/reader036/viewer/2022081514/5a4d1b967f8b9ab0599c396b/html5/thumbnails/18.jpg)
How to GRAPH a QUADRATIC FUNCTION:
1. Get the Quadratic Function in EQUATION form.
2. Find the VERTEX X Coordinate
3. Make a table of 5 X points, with the 3rd Point being the VERTEX.
4. Find the Y Coordinate for each X Point
5. CONNECT the Points.
ba2
(x + 2)2 – 9
![Page 19: Lesson: Objectives: 5.1 Solving Quadratic Equations - Graphing DESCRIBE the Elements of the GRAPH of a Quadratic Equation DETERMINE a Standard Approach.](https://reader036.fdocuments.in/reader036/viewer/2022081514/5a4d1b967f8b9ab0599c396b/html5/thumbnails/19.jpg)
How to GRAPH a QUADRATIC FUNCTION:
1. Get the Quadratic Function in EQUATION form.
2. Find the VERTEX X Coordinate
3. Make a table of 5 X points, with the 3rd Point being the VERTEX.
4. Find the Y Coordinate for each X Point
5. CONNECT the Points.
ba2
x2 – 4x + 4
![Page 20: Lesson: Objectives: 5.1 Solving Quadratic Equations - Graphing DESCRIBE the Elements of the GRAPH of a Quadratic Equation DETERMINE a Standard Approach.](https://reader036.fdocuments.in/reader036/viewer/2022081514/5a4d1b967f8b9ab0599c396b/html5/thumbnails/20.jpg)
How to GRAPH a QUADRATIC FUNCTION:
1. Get the Quadratic Function in EQUATION form.
2. Find the VERTEX X Coordinate
3. Make a table of 5 X points, with the 3rd Point being the VERTEX.
4. Find the Y Coordinate for each X Point
5. CONNECT the Points.
ba2
x2 – 3x + 6
![Page 21: Lesson: Objectives: 5.1 Solving Quadratic Equations - Graphing DESCRIBE the Elements of the GRAPH of a Quadratic Equation DETERMINE a Standard Approach.](https://reader036.fdocuments.in/reader036/viewer/2022081514/5a4d1b967f8b9ab0599c396b/html5/thumbnails/21.jpg)
How to GRAPH a QUADRATIC FUNCTION:
1. Get the Quadratic Function in EQUATION form.
2. Find the VERTEX X Coordinate
3. Make a table of 5 X points, with the 3rd Point being the VERTEX.
4. Find the Y Coordinate for each X Point
5. CONNECT the Points.
ba2
x2 – 9
![Page 22: Lesson: Objectives: 5.1 Solving Quadratic Equations - Graphing DESCRIBE the Elements of the GRAPH of a Quadratic Equation DETERMINE a Standard Approach.](https://reader036.fdocuments.in/reader036/viewer/2022081514/5a4d1b967f8b9ab0599c396b/html5/thumbnails/22.jpg)
Using a GRAPHING CALCULATOR to GRAPH Quadratic Functions
1. Get the function in y = form. Enter it in y =
2. Look at the GRAPH
3. Use 2nd Calc, Value to complete the X, Y table
4. If needed, use 2nd Calc to find ROOTS
5. If needed, use 2nd Calc to find the VERTEX by finding the MINIMUM or MAXIMUM
![Page 23: Lesson: Objectives: 5.1 Solving Quadratic Equations - Graphing DESCRIBE the Elements of the GRAPH of a Quadratic Equation DETERMINE a Standard Approach.](https://reader036.fdocuments.in/reader036/viewer/2022081514/5a4d1b967f8b9ab0599c396b/html5/thumbnails/23.jpg)
Using a GRAPHING CALCULATOR to GRAPH Quadratic Functions
1. Get the function in y = form. Enter it in y =
2. Look at the GRAPH
3. Use 2nd Calc, Value to complete the X, Y table
4. If needed, use 2nd Calc to find ROOTS
5. If needed, use 2nd Calc to find the VERTEX by finding the MINIMUM or MAXIMUM
m2 + 3m = 4
![Page 24: Lesson: Objectives: 5.1 Solving Quadratic Equations - Graphing DESCRIBE the Elements of the GRAPH of a Quadratic Equation DETERMINE a Standard Approach.](https://reader036.fdocuments.in/reader036/viewer/2022081514/5a4d1b967f8b9ab0599c396b/html5/thumbnails/24.jpg)
Using a GRAPHING CALCULATOR to GRAPH Quadratic Functions
1. Get the function in y = form. Enter it in y =
2. Look at the GRAPH
3. Use 2nd Calc, Value to complete the X, Y table
4. If needed, use 2nd Calc to find ROOTS
5. If needed, use 2nd Calc to find the VERTEX by finding the MINIMUM or MAXIMUM
4v2 – 8v – 5 = t
![Page 25: Lesson: Objectives: 5.1 Solving Quadratic Equations - Graphing DESCRIBE the Elements of the GRAPH of a Quadratic Equation DETERMINE a Standard Approach.](https://reader036.fdocuments.in/reader036/viewer/2022081514/5a4d1b967f8b9ab0599c396b/html5/thumbnails/25.jpg)
Using a GRAPHING CALCULATOR to GRAPH Quadratic Functions
1. Get the function in y = form. Enter it in y =
2. Look at the GRAPH
3. Use 2nd Calc, Value to complete the X, Y table
4. If needed, use 2nd Calc to find ROOTS
5. If needed, use 2nd Calc to find the VERTEX by finding the MINIMUM or MAXIMUM
Y =- 4x2 – 8x – 9
![Page 26: Lesson: Objectives: 5.1 Solving Quadratic Equations - Graphing DESCRIBE the Elements of the GRAPH of a Quadratic Equation DETERMINE a Standard Approach.](https://reader036.fdocuments.in/reader036/viewer/2022081514/5a4d1b967f8b9ab0599c396b/html5/thumbnails/26.jpg)
Using a GRAPHING CALCULATOR to GRAPH Quadratic Functions
1. Get the function in y = form. Enter it in y =
2. Look at the GRAPH
3. Use 2nd Calc, Value to complete the X, Y table
4. If needed, use 2nd Calc to find ROOTS
5. If needed, use 2nd Calc to find the VERTEX by finding the MINIMUM or MAXIMUM
Y = 4x2 + 11
![Page 27: Lesson: Objectives: 5.1 Solving Quadratic Equations - Graphing DESCRIBE the Elements of the GRAPH of a Quadratic Equation DETERMINE a Standard Approach.](https://reader036.fdocuments.in/reader036/viewer/2022081514/5a4d1b967f8b9ab0599c396b/html5/thumbnails/27.jpg)
Using a GRAPHING CALCULATOR to GRAPH Quadratic Functions
1. Get the function in y = form. Enter it in y =
2. Look at the GRAPH
3. Use 2nd Calc, Value to complete the X, Y table
4. If needed, use 2nd Calc to find ROOTS
5. If needed, use 2nd Calc to find the VERTEX by finding the MINIMUM or MAXIMUM
Y =2x2 – 6x – 4
![Page 28: Lesson: Objectives: 5.1 Solving Quadratic Equations - Graphing DESCRIBE the Elements of the GRAPH of a Quadratic Equation DETERMINE a Standard Approach.](https://reader036.fdocuments.in/reader036/viewer/2022081514/5a4d1b967f8b9ab0599c396b/html5/thumbnails/28.jpg)
Using a GRAPHING CALCULATOR to GRAPH Quadratic Functions
1. Get the function in y = form. Enter it in y =
2. Look at the GRAPH
3. Use 2nd Calc, Value to complete the X, Y table
4. If needed, use 2nd Calc to find ROOTS
5. If needed, use 2nd Calc to find the VERTEX by finding the MINIMUM or MAXIMUM
Y =-2x2 – x – 15
![Page 29: Lesson: Objectives: 5.1 Solving Quadratic Equations - Graphing DESCRIBE the Elements of the GRAPH of a Quadratic Equation DETERMINE a Standard Approach.](https://reader036.fdocuments.in/reader036/viewer/2022081514/5a4d1b967f8b9ab0599c396b/html5/thumbnails/29.jpg)
Using a GRAPHING CALCULATOR to GRAPH Quadratic Functions
1. Get the function in y = form. Enter it in y =
2. Look at the GRAPH
3. Use 2nd Calc, Value to complete the X, Y table
4. If needed, use 2nd Calc to find ROOTS
5. If needed, use 2nd Calc to find the VERTEX by finding the MINIMUM or MAXIMUM
Y =x2 + 30x + 225
![Page 30: Lesson: Objectives: 5.1 Solving Quadratic Equations - Graphing DESCRIBE the Elements of the GRAPH of a Quadratic Equation DETERMINE a Standard Approach.](https://reader036.fdocuments.in/reader036/viewer/2022081514/5a4d1b967f8b9ab0599c396b/html5/thumbnails/30.jpg)
Using a GRAPHING CALCULATOR to GRAPH Quadratic Functions
1. Get the function in y = form. Enter it in y =
2. Look at the GRAPH
3. Use 2nd Calc, Value to complete the X, Y table
4. If needed, use 2nd Calc to find ROOTS
5. If needed, use 2nd Calc to find the VERTEX by finding the MINIMUM or MAXIMUM