6. 1 graphing quadratics

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6. 1 graphing quadratics

  1. 1. Graphing Quadratic Functions (Ch 6) <ul><li>Definitions </li></ul><ul><li>Steps for graphing </li></ul>
  2. 2. Quadratic Function <ul><li>A function of the form y=ax 2 +bx+c where a ≠0 making a u-shaped graph called a parabola . </li></ul>Example quadratic equation:
  3. 3. Vertex- <ul><li>The lowest or highest point </li></ul><ul><li>of a parabola. </li></ul><ul><li>Vertex </li></ul><ul><li>Axis of symmetry- </li></ul><ul><li>The vertical line through the vertex of the parabola. </li></ul>Axis of Symmetry
  4. 4. Standard Form Equation <ul><li>y=ax 2 + bx + c </li></ul><ul><li>If a is positive , u opens up </li></ul><ul><li>If a is negative , u opens down </li></ul><ul><li>The x-coordinate of the vertex is at </li></ul><ul><li>To find the y-coordinate of the vertex, plug the x-coordinate into the given eqn. </li></ul><ul><li>The axis of symmetry is the vertical line x= </li></ul><ul><li>Choose 2 x-values on either side of the vertex x-coordinate. Use the eqn to find the corresponding y-values. </li></ul><ul><li>Graph and label the 5 points and axis of symmetry on a coordinate plane. Connect the points with a smooth curve. </li></ul>
  5. 5. Example 1 : Graph y=2x 2 -8x+6 <ul><li>a=2 Since a is positive the parabola will open up. </li></ul><ul><li>Vertex: use </li></ul><ul><li>b=-8 and a=2 </li></ul><ul><li>Vertex is: (2,-2) </li></ul><ul><li>Axis of symmetry is the vertical line x=2 </li></ul><ul><li>Table of values for other points: x y </li></ul><ul><li> 0 6 </li></ul><ul><li> 1 0 </li></ul><ul><li> 2 -2 </li></ul><ul><li> 3 0 </li></ul><ul><li> 4 6 </li></ul><ul><li>* Graph! </li></ul>x=2
  6. 6. Now you try one! y=-x 2 +x+12 * Open up or down? * Vertex? * Axis of symmetry? * Table of values with 5 points?
  7. 7. (-1,10) (-2,6) (2,10) (3,6) X = .5 (.5,12)
  8. 8. Changing from vertex or intercepts form to standard form <ul><li>The key is to use Double Distribution! </li></ul><ul><li>Ex: y=-(x+4)(x-9) Ex: y=3(x-1) 2 +8 </li></ul><ul><li> =-(x 2 -9x+4x-36) =3(x-1)(x-1)+8 </li></ul><ul><li> =-(x 2 -5x-36) =3(x 2 -x-x+1)+8 </li></ul><ul><li>y=-x 2 +5x+36 =3(x 2 -2x+1)+8 </li></ul><ul><li> =3x 2 -6x+3+8 </li></ul><ul><li> y=3x 2 -6x+11 </li></ul>

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