oct14/09 dmcimath precal30s
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oct14/09 dmcimath precal30s Document Transcript

  • 1. Solving for Roots By Completing the square • You can complete the square by adding a constant to both  sides of the equation • Add the constant that will turn the quadratic into a perfect  square • Take the square root of both sides • Solve for x Ex. Solve x2 ­ 4x + 2 = 0  1
  • 2. When the leading coefficient is not equal to one • Divide both sides of the equation by the  coefficient a before completing the square Ex. Solve by completing the square 2x2 ­ 6x ­7 = 0 2
  • 3. General Solution to Quadratics by  Completing the Square (building the quadratic formula) Solve for x by completing the square ax2 + bx +c = 0 3
  • 4. The completing square allows us to find that we can find the  solutions using the  Quadratic Formula   You can use the quadratic formula to solve any quadratic equation. To use the equation you first need to set up the equation in  standard form   ax2 + bx + c = 0 Then you can substitute a, b, and c into the formula 4
  • 5. 5
  • 6. Ex. Sove   x2 + 3x ­ 9 = 0 6
  • 7. If you remember from our quadratics unit, we can  find the x value at the vertex, and the axis of  symmetry by  h =  The quadratic formula can be represented by two  fractions. The first part is the h value. The second part is the horizontal distance from the  axis of symmetry to the x intercepts in both the  positive  and negative direction. 7