Warm Up  Get your tracking sheet and homework out. Get started on the following warm up problems: 1. Sketch the graph of the polynomial function. 2. Complete the square to find the roots 3. Put the function from #2 in vertex form. 4. Find the roots and the vertex of the following function using a method of your choice.

Homework Answers

 Completing the Square and the Quadratic Formula

Problem to think about:  Mrs. Inscoe is going into the Bobble-Head doll business and she thinks she can get rich. The problem is, she has no business knowledge at all, so she really needs your help. You have done some research, and know that her Profit (P(x)) depends on the price she charges (x), and can be represented by the function  P(x) = x – x 2  What price should she charge to maximize her profit so she can buy a fancy beach house?  What would be a really dumb price for her to charge (the price or prices where she would earn $0)?

Vertex Form and Completing the Square Revisited  We can complete the square to kill two birds with ONE stone:  Find the roots  AND put the equation in vertex form so we also know the vertex.  (Disclaimer: no birds will be harmed during AFM today)

Complete the square to find the vertex and roots of the following functions: 2x 2 – 8x + 6 = 0

You Try a Few  Complete the square for each of the functions on your sheet.  Write each equation in vertex form, and list the zeroes.

Label the Roots and Vertex of the Following Graphs

Label the Roots and the Vertex of this Graph

Complex Roots:  Roots that are “imaginary”  Exist for quadratic functions that do not touch the x-axis  There is NO x that will make f(x) = 0  …No REAL one that is  How do we know if a quadratic function has imaginary roots?  It does not touch the x-axis  When we try to solve it to complete the square, we have to take the square root of a negative number.

Ways to find the roots  Factoring  Completing the Square  Using “trace” in your calculator  The Quadratic Formula

Method:FactoringCompleting the Square “Trace” in Calculator Quadratic Formula Pros: Cons:

What is the Quadratic Formula?  Here’s the proof: graphing-quadratics-parabolas/11-proof-quadratic- forumula-01.htm

Finding Roots with the Quadratic Formula:

You Practice:  Find the roots of the following quadratic functions in your notes using the quadratic formula:

Mixed Practice  Complete the practice problems at the bottom of your worksheet on a separate sheet of paper.  To earn your class work stamp for today, you must complete: ________ problems.  Whatever you do not finish in class is homework

Homework  Complete the practice problems you didn’t finish in class.

Exit Ticket 1. Use the quadratic formula to find the roots of the following function: 1. In your own words, what is a complex root? (And how do we know if a function has real or complex roots?) 1. Complete the square to write the equation in vertex form AND find the roots:

Test Return  Make sure I added correctly with the points I took off.  What questions do you have?  Give these back to me before you walk out of the room today!  Problems to go over: #20 – 30