Do NowDraw a quick sketch of the following

polynomials. Name any changes that have occurred.

3

2

3

2

3

2

)(

)(

3

1)(

3

1)(

2)(

2)(

xxn

xxm

xxk

xxh

xxg

xxf

Today’s Learning Targets-Graph and translate polynomial parent

functions in the form f(x)=ax^n-Graph and name the vertex and axis

of symmetry of a quadratic function-Apply methods of solving to real-life

problems

Polynomial parent functionsStandard formFollows same rules from chapter 2 (a, b, c, d,

flip translations)Even Family Odd Familya>0 a<0 a>0

a<0

naxxf )(

Quick Sketch

QuadraticsSpecific form called “vertex form” of writing

translated equationThe point (h, k) is the vertex, lowest or

highest pointAxis of symmetry at vertical line x=h (use

coordinate or vertex)Example:

khxaxf 2)()(

3)2(1)( 2 xxf 5)3()( 2 xxf

Find the vertex & axis of symmetry of the following parabolas

3)4(2)( 2 xxf 2)1()( 2 xxf

Axis of symmetry and vertex in standard form Given , standard form, use the

following equations for Axis of symmetry (x=h)-- Vertex (h,k)

Find value of x-coordinate of vertex, then use as input to find y-coordinate of vertex

cbxaxxf 2)(

a

bhx

2

)(hfk

Example: Find vertex and axis in standard form

542)( 2 xxxf 8123)( 2 xxxf

Max and MinWhy is the vertex important?

Applications that use quadratic equations to model where maximizing or minimizing is importantMaximize profitMinimize lossesMaximize areaProjectile motion- maximum height

ApplicationsMs. K opened a taco stand and found that her

daily costs are approximated by

Where C(x) is the cost in $$ to sell x units of tacos. Find the number of units of tacos she should sell to minimize her costs. What is minimum cost?

61040)( 2 xxxC

HW We have not finished the section yet3.1 #12-22 even, 50-62 even3.4 #1-8, 10-16 even, 22-34 even, 66, 68, 101

Today covers 3.1 & 1-8, 10-16, 30-34NOT end behavior