1. Daily Check #2 Factor the following quadratics... a) b) c)

2. Questions over hw? He didn’t see the ewe turn!

3. Math II Day 5 (1-10-11) Standard MM2A3 b – Graph quadratic functions as transformations of the function f(x) = x 2 Today’s Question: How to we graph a parabola using vertex form?

4. Intro to Parabolas

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10. 3.2 Graphing Quadratic Functions in Vertex or Intercept Form Definitions Definitions 3 Forms 3 Forms Graphing in vertex form Graphing in vertex form Examples Examples Changing between eqn. forms Changing between eqn. forms

11. Quadratic Function A function of the form y=ax 2 +bx+c where a≠0 making a u-shaped graph called a parabola. A function of the form y=ax 2 +bx+c where a≠0 making a u-shaped graph called a parabola. Example quadratic equation:

12. x – intercepts (-3,0) (1,0) y – intercept (0,6) vertex (-1,8) Interval of IncreaseInterval of Decrease

13. Vertex- The lowest or highest point of a parabola. Vertex Axis of symmetry- The vertical line through the vertex of the parabola. Axis of Symmetry

14. Example Website let’s look at some parabolas scroll all the way down to the bottom examples Quadratics in Action Quadratics in Action Quadratics in Action Quadratics in Action

15. The 3 Forms of Quadratics FactoredVertex Form Standard Form (x+4)(x-9)(x-2.5) 2 - 42.25x 2 -5x-36

16. Vertex Form Equation y=a(x-h)2+k

17. y=a(x-h)2+k If a is positive, parabola opens up If a is negative, parabola opens down. The vertex is the point (h,k). If a > 1 the parabola gets skinny If a < 1 the parabola gets fatter The vertex is the point (h,k). The axis of symmetry is the vertical line x=h.

18. Tip for the Vertex (x – h) 2 + k (x – h) 2 + k The y doesn’t lie The y doesn’t lie But the x does – we must change its sign. But the x does – we must change its sign. (x – 3) 2 + 7 (x – 3) 2 + 7 –Vertex will be at (3,7)

19. Now You Try. Where is the vertex of Where is the vertex of (x – 2) 2 + 8 (x – 2) 2 + 8 (x + 5) 2 + 7 (x + 5) 2 + 7 (x + 4) 2 - 2 (x + 4) 2 - 2 (2,8) (-5,7) (-4,-2)

20. Vertex Form  Each function we just looked at can be written in the form (x – h) 2 + k, where (h, k) is the vertex of the parabola, and x = h is its axis of symmetry.  (x – h) 2 + k – vertex form EquationVertex Axis of Symmetry y = x 2 or y = (x – 0) 2 + 0 (0, 0) x = 0 y = x 2 + 2 or y = (x – 0) 2 + 2 (0, 2) x = 0 y = (x – 3) 2 or y = (x – 3) 2 + 0 (3, 0) x = 3

21. Hold Up…..Wait a minute let’s go back to that website and identify equations http://www.analyzemath.com/quadraticg/quadraticg.htm

22. Example: Graph y=-.5(x+3) 2 +4 a is negative (a = -.5), so parabola opens down. a is negative (a = -.5), so parabola opens down. Vertex is (h,k) or (-3,4) Vertex is (h,k) or (-3,4) Axis of symmetry is the vertical line x = -3 Axis of symmetry is the vertical line x = -3 Table of values Table of values x -.5(x+3) 2 +4 y (x, y) Vertex (-3,4) (-4,3.5) (-5,2) (-2,3.5) (-1,2) x=-3 -1 -.5(-1+3) 2 +4 2 (-1,2) -2 -.5(-2+3) 2 +4 2 (-2,3.5) -4 -.5(-4+3) 2 +4 2 (-3,3.5) -5 -.5(-5+3) 2 +4 2 (-4,2)

23. Let’s do together Analyze and Graph: Analyze and Graph: y = (x + 4) 2 - 3. y = (x + 4) 2 - 3. (-4,-3)

24. Now you try one! y=2(x-1) 2 +3 Open up or down? Open up or down? Vertex? Vertex? Axis of symmetry? Axis of symmetry? Table of values? Table of values?

25. (-1, 11) (0,5) (1,3) (2,5) (3,11) X = 1

26. Classwork Page 67 #11 - 18

27. Homework Book Page 65 #13-18