1. January 18 th copyright2009merrydavidson Happy Birthday to: Maggie Neece 1/12 Mary Parrett 1/13 and today: Martin Moreno & Blake Gober

2. Quadratic Functions VERTEX form: where is the vertex. Opens up Opens down What is the vertex?

3. All quadratic functions are symmetric over a line called the axis of symmetry. x = 3

4. Graph the following w/out a calculator. f(x) = -2(x + 3) 2 + 4 Start with the vertex. Draw in the AOS. Make a T-chart with points on either side of the vertex. Remember points are symmetric over the AOS. Find y-intercept.

5. Reviewing Vertex Form by “Completing the Square” f(x) = x 2 + 8x + 11 Step 1:Group the 1 st 2 terms Step 2: Add & subtract blanks Step 3: ½ the middle term squared Step 4: factor Step 5: simplify f(x) = (x 2 + 8x) + 11 f(x) = (x 2 + 8x + _) + 11 - _ 4242 4242 f(x) = (x + 4) 2 + 11 - 16 f(x) = (x + 4) 2 - 5

6. Changing to Vertex Form by “Completing the Square” 2) f(x) = x 2 - 10x + 22 YOUR TURN f(x) = (x – 5) 2 - 3 What is the vertex? (5, -3)

7. 3) f(x) = 2x 2 + 8x + 7 Step 1:Group the 1 st 2 terms Step 2: Factor out the 2 f(x) = (2x 2 + 8x) + 7 f(x) = 2(x 2 + 4x) + 7 f(x) = 2(x 2 + 4x + _) + 7 - _(2)2 2 f(x) = 2(x + 2) 2 + 7 - 8 f(x) = 2(x + 2) 2 - 1

8. 4) f(x) = -x 2 - 4x + 21 f(x) = -(x 2 + 4x + _) + 21 - _(-1) 2 2 f(x) = -(x + 2) 2 + 21 + 4 f(x) = -(x + 2) 2 + 25 YOUR TURN

9. 5) 2y = 5x 2 + 10x + 7 2y = 5(x 2 + 2x + _) + 7 - _(5) 1212 1212 2y = 5(x + 1) 2 + 2 SAVE the 2 for later. NOW divide by 2.

10. Homework worksheet SHOW ALL WORK NEATLY.