do now draw a quick sketch of the following polynomials. name any changes that have occurred
TRANSCRIPT
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 )(
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
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
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