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Daily Check #2

Daily Check #2. Factor the following quadratics... a) b) c). Questions over hw?. He didn’t see the ewe turn!. 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:

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Daily Check #2

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

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

  3. Math IIDay 5 (1-10-11) • Standard MM2A3 • b – Graph quadratic functions as transformations of the function f(x) = x2 • Today’s Question: • How to we graph a parabola using vertex form?

  4. Intro to Parabolas

  5. Dude Perfect Video

  6. 3.2 Graphing Quadratic Functions in Vertex or Intercept Form • Definitions • 3 Forms • Graphing in vertex form • Examples • Changing between eqn. forms

  7. Quadratic Function • A function of the form y=ax2+bx+c where a≠0 making a u-shaped graph called a parabola. Example quadratic equation:

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

  9. 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

  10. Example Websitelet’s look at some parabolasscroll all the way down to the bottom examples • Quadratics in Action

  11. The 3 Forms of Quadratics

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

  13. Vertex Form Equation 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.

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

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

  16. 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

  17. Hold Up…..Wait a minutelet’s go back to that websiteand identify equations http://www.analyzemath.com/quadraticg/quadraticg.htm

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

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

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

  21. (-1, 11) (3,11) X = 1 (0,5) (2,5) (1,3)

  22. Classwork Page 67 #11 - 18

  23. Homework Book Page 65 #13-18

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