Post on 19-Jan-2018
description
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
ALGEBRA II 5.1-5.2
TERMS Related to QUADRATIC Functions
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
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
ALGEBRA II 5.1-5.2
The GRAPH of a QUADRATIC Function is a
PARABOLA
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
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
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
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.
ALGEBRA II
QUADRATIC FUNCTION
A FUNCTION described by an EQUATION that can be written in the form:
f(x) = ax2 + bx + c
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
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.
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
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)
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 + 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
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
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
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
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
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
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
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
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
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
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
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
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
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
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