Do Now Draw a quick sketch of the following polynomials. Name any changes that have occurred.

- 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 functions Standard form Follows same rules from chapter 2 (a, b, c, d, flip translations) Even FamilyOdd Family a>0 a 0a<0

Quick Sketch

Quadratics Specific form called “vertex form” of writing translated equation The point (h, k) is the vertex, lowest or highest point Axis of symmetry at vertical line x=h (use coordinate or vertex) Example:

Find the vertex & axis of symmetry of the following parabolas

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

Example: Find vertex and axis in standard form

Max and Min Why is the vertex important? Applications that use quadratic equations to model where maximizing or minimizing is important Maximize profit Minimize losses Maximize area Projectile motion- maximum height

Applications Ms. 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?

HW We have not finished the section yet 3.1 #12-22 even, even 3.4 #1-8, even, even, 66, 68, 101 Today covers 3.1 & 1-8, 10-16, NOT end behavior