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Math I

Math I. UNIT QUESTION: What is a quadratic function? Standard: MM2A3, MM2A4 Today’s Question: How do you graph quadratic functions in vertex form? Standard: MM2A3.b. 6.6 Graphing Quadratic Functions in Vertex or Intercept Form. Definitions 3 Forms Steps for graphing each form Examples.

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Math I

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  1. Math I UNIT QUESTION: What is a quadratic function? Standard: MM2A3, MM2A4 Today’s Question: How do you graph quadratic functions in vertex form? Standard: MM2A3.b.

  2. 6.6 Graphing Quadratic Functions in Vertex or Intercept Form • Definitions • 3 Forms • Steps for graphing each form • Examples

  3. Daily Check • Factor: 3x2 + 10x + 8 • Factor and Solve: 2x2 - 7x + 3 = 0

  4. Review: Quadratic Parent Parent Name: Quadratic Parent Equation: 4 Domain: 1 Range : 0 Vertex: 1 Axis of Symmetry: 4 General Equation (in Vertex Form) Domain: Range : Axis of Symmetry: Vertex:

  5. AAT-A Date: 2/17/14 SWBAT write quadratic equations in vertex form. • Do Now: Review Questions pg 336 #1-50, evens • HW Requests: pg 303 #42-49; Pg 310 #15-37 odds Worksheets for homework Skills Practice pg 340 Worksheet Quadratics Graphing TBD • HW: Skills Practice Vertex form 6.6 • Announcements: Life Is Just A MinuteLife is just a minute—only sixty seconds in it.Forced upon you—can't refuse it.Didn't seek it—didn't choose it.But it's up to you to use it.You must suffer if you lose it.Give an account if you abuse it.Just a tiny, little minute,But eternity is in it!By Dr. Benjamin Elijah Mays, Past President of Morehouse College

  6. Writing a Quadratic Function in Vertex Form Steps: 5. Solve for y the equation will be in vertex form. 1. Write the function in standard form. 2. Set it up to complete the square. 3. Add the square to both sides of the = sign. 4. Write the trinomial as a binomial squared.

  7. Writing a Quadratic Function in Vertex Form Example 1: Write the function in vertex form and identify its vertex. 1. Write the function in standard form. 2. Set it up to complete the square.

  8. Writing a Quadratic Function in Vertex Form 3. Add the square to both sides of the = sign. 5. Solve for y the equation will be in vertex form. 4. Write the trinomial as a binomial squared. Vertex:

  9. Practice: Write a quadratic function in vertex form and identify its vertex. P1:

  10. Practice: Write a quadratic function in vertex form and identify its vertex. P2:

  11. Writing a Quadratic Function in Vertex Form Example 2: Factor, write the function in vertex form, and identify its vertex. 1. Write the function in standard form. 2. Factor the first two terms. 3. Set it up to complete the square.

  12. Writing a Quadratic Function in Vertex Form 4. Add the square to both sides of the = sign. 6. Solve for y the equation will be in vertex form. 5. Write the trinomial as a binomial squared. Vertex:

  13. Practice: Write a quadratic function in vertex form and identify its vertex. P3:

  14. Practice: Write a quadratic function in vertex form and identify its vertex. P4: Vertex:

  15. Writing a Quadratic Function in Vertex Form Example 3: Write the function, using fractions, in vertex form, and identify its vertex. 1. Write the function in standard form. 2. Set it up to complete the square.

  16. Writing a Quadratic Function in Vertex Form 3. Add the square to both sides of the = sign. Look! Be careful with the added term when a<1 5. Solve for y the equation will be in vertex form. 4. Write the trinomial as a binomial squared. Vertex:

  17. Practice: Write a quadratic function in vertex form and identify its vertex. P5: Vertex:

  18. Independent Practice Write each function in vertex form and identify its vertex.

  19. 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:

  20. 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

  21. 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). • The axis of symmetry is the vertical line x=h. • Don’t forget about 2 points on either side of the vertex! (5 points total!)

  22. 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

  23. Example 1: Graph y = (x + 2)2 + 1 • Analyze y = (x + 2)2 + 1. • Step 1 Plot the vertex (-2 , 1) • Step 2 Draw the axis of symmetry, x = -2. • Step 3 Find and plot two points on one side, such as (-1, 2) and (0 , 5). • Step 4 Use symmetry to complete the graph, or find two points on the left side of the vertex.

  24. Your Turn! • Analyze and Graph: y = (x + 4)2 - 3. (-4,-3)

  25. Example 2: 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 y -1 2 -2 3.5 -3 4 -4 3.5 -5 2 Vertex (-3,4) (-4,3.5) (-2,3.5) (-5,2) (-1,2) x=-3

  26. Now you try one! y=2(x-1)2+3 • Open up or down? • Vertex? • Axis of symmetry? • Table of values with 4 points (other than the vertex?

  27. (-1, 11) (3,11) X = 1 (0,5) (2,5) (1,3)

  28. Intercept Form Equation y=a(x-p)(x-q) • The x-intercepts are the points (p,0) and (q,0). • The axis of symmetry is the vertical line x= • The x-coordinate of the vertex is • To find the y-coordinate of the vertex, plug the x-coord. into the equation and solve for y. • If a is positive, parabola opens up If a is negative, parabola opens down.

  29. Example 3: Graph y=-(x+2)(x-4) • The axis of symmetry is the vertical line x=1 (from the x-coord. of the vertex) • Since a is negative, parabola opens down. • The x-intercepts are (-2,0) and (4,0) • To find the x-coord. of the vertex, use • To find the y-coord., plug 1 in for x. • Vertex (1,9) (1,9) (-2,0) (4,0) x=1

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

  31. x=1 (-1,0) (3,0) (1,-8)

  32. Changing from vertex or intercepts form to standard form • The key is to FOIL! (first, outside, inside, last) • Ex: y=-(x+4)(x-9) Ex: y=3(x-1)2+8 =-(x2-9x+4x-36) =3(x-1)(x-1)+8 =-(x2-5x-36) =3(x2-x-x+1)+8 y=-x2+5x+36 =3(x2-2x+1)+8 =3x2-6x+3+8 y=3x2-6x+11

  33. Challenge Problem • Write the equation of the graph in vertex form.

  34. Assignment Day 1 -p. 65 #4,6,7,9,13,16 and Review for Quiz Day 2 – p. 67 #4,5,7,9,11-14 We will not do intercept form.

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