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3.2 Graphing Quadratic Functions in Vertex or Intercept Form

3.2 Graphing Quadratic Functions in Vertex or Intercept Form. Definitions 3 Forms Graphing in vertex form Examples Changing between eqn. forms. Quadratic Function. A function of the form y=ax 2 +bx+c where a ≠0 making a u-shaped graph called a parabola. Example quadratic equation:.

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3.2 Graphing Quadratic Functions in Vertex or Intercept Form

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  1. 3.2 Graphing Quadratic Functions in Vertex or Intercept Form • Definitions • 3 Forms • Graphing in vertex form • Examples • Changing between eqn. forms

  2. 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:

  3. 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

  4. 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.

  5. 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

  6. Example 1: Graph • 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.

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

  8. 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

  9. Now you try one! y=2(x-1)2+3 • Open up or down? • Vertex? • Axis of symmetry? • Table of values with 5 points?

  10. (-1, 11) (3,11) X = 1 (0,5) (2,5) (1,3)

  11. Changing from vertex or intercepts form to standard form • The key is to follow ORDER OF OPERATIONS • 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

  12. Changing from vertex or intercepts form to standard form • Practice: • 1: y = 3(x-4)(x+2) • 2: y = -2(x-3)2 - 5

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

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