4 January 2010

Algebra 2

Bellringer:Solve for x: 10y + 4x = 14

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)_, _______, _______

Homework

Find the vertex of the following equations. Then make and x/y chart using the following values for x: -3, 1, -2, 3

1. 2x2-3x+5=152. -x2+x-1=-53. 3x2+2x+8