Embed Size (px)
Citation preview
3 January 2010
Algebra 2
Bellringer:Solve for x: 10 + 4x = 14
Agenda:
• Progress Report Information• Classroom Standards and Expectations• Graphing Quadratic Functions• Exit Ticket
Progress Report Information
Classroom Standards and Expectations
Notes: Graphing Quadratic FunctionsFunctions Functions are equations written in
the form f(x) = ______
Notes: Graphing Quadratic FunctionsFunctions Functions are equations written in
the form f(x) = ______
Example: f(x) = 5 or f(x) = 3x + 9
Notes: Graphing Quadratic FunctionsFunctions
Quadratic Functions
Functions are equations written in the form f(x) = ______
Example: f(x) = 5 or f(x) = 3x + 9
Quadratic functions are functions that have a degree of 2.
Notes: Graphing Quadratic FunctionsFunctions
Quadratic Functions
Functions are equations written in the form f(x) = ______
Example: f(x) = 5 or f(x) = 3x + 9
Quadratic functions are functions that have a degree of 2.
Example: f(x) = 2x2 + 4x – 9
Notes: Graphing Quadratic FunctionsFunctions
Quadratic Functions
Functions are equations written in the form f(x) = ______
Example: f(x) = 5 or f(x) = 3x + 9
Quadratic functions are functions that have a degree of 2.
Example: f(x) = 2x2 + 4x – 9
Why is f(x) = x3 + x2 + 10 not quadratic?
Notes: Graphing Quadratic FunctionsFunctions
Quadratic Functions
Functions are equations written in the form f(x) = ______
Example: f(x) = 5 or f(x) = 3x + 9
Quadratic functions are functions that have a degree of 2.
Example: f(x) = 2x2 + 4x – 9
Why is f(x) = x3 + x2 + 10 not quadratic?Why is f(x) = x + 10 not quadratic?
Notes: Graphing Quadratic FunctionsFind the
vertex of a quadratic Function
Mathematics.FUN.401
Use the formula x = -b to find the vertex. 2a
b = # in front of xa = # in front of x2
f(x) = 2x2 + 8x -9
x = - 8 2(2) x = -2
f(x) = 2x2 + 8x -9f(x) = 2(-2)2 + 8(-2) -9 = -17
vertex = (-2, -17)
Notes: Graphing Quadratic FunctionsMaking a
tableMathematics.GRE.605
Using the vertex you just found, make a table of (x,y) values
* put the vertex on the middle line
x 2x2 + 8x - 9 y (x,y)
-2 2(-2)2 + 8(-2) -9 -17 (-2, -17)
Notes: Graphing Quadratic FunctionsMaking a
tableMathematics.GRE.605
Using the vertex you just found, make a table of (x,y) values
* pick any two numbers greater than the x value of your vertex (-2)
x 2x2 + 8x - 9 y (x,y)
0
-1
-2 2(-2)2 + 8(-2) -9 -17 (-2, -17)
Notes: Graphing Quadratic FunctionsMaking a
tableMathematics.GRE.605
Using the vertex you just found, make a table of (x,y) values
* pick any two numbers less than the x value of your vertex (-2)
x 2x2 + 8x - 9 y (x,y)
0
-1
-2 2(-2)2 + 8(-2) -9 -17 (-2, -17)
-3
-4
Notes: Graphing Quadratic FunctionsMaking a
tableMathematics.GRE.605
Using the vertex you just found, make a table of (x,y) values
* complete the rest of the table by substituting your x values into your function
x 2x2 + 8x - 9 y (x,y)
0 2(0)2 + 8(0) -9 -9 (0,-9)
-1 2(-1)2 + 8(-1) -9 -15 (-1,-15)
-2 2(-2)2 + 8(-2) -9 -17 (-2, -17)
-3 2(-3)2 + 8(-3) -9 -15 (-3,-15)
-4 2(-4)2 + 8(-4) -9 -9 (-4,-9)
Notes: Graphing Quadratic FunctionsGraphing
a Q.F. Mathematics.GRE.605
Using the (x,y) pairs you just found, plot the points on a graph.
(0,-9) (-1,-15) (-2, -17) (-3,-15) (-4,-9)
Notes: Graphing Quadratic FunctionsGraphing
a Q.F. Mathematics.GRE.605
Connect the five points you have plotted.
PHEW, Finally done!!!!!
Guided Practice:Graph f(x) = x2 – 4x – 3
1. Find the Vertex
f(x) = x2 – 4x – 3
a = ________ b = ________
x = - ( ) 2( ) x = ______
2. Evaluate x2 – 4x – 3 to find y
x = _____ ( )2 – 4( ) – 3
( )2 – 4( ) – 3 = _______ This is your y value
y = _______
Using the vertex you just found, make a table of (x,y) values
x x2 – 4x – 3 y (x,y)
2 (2)2 – 4(2) - 3 -7 (2, -7)
4. List the 5 points you are going to graph:
_______, _______, __(2,-7)_, _______, _______
