Quadratic Formula

  1.  \rhd The quadratic formula (16:31) The solution to three equations using the quadratic formula, and the relationship of the solutions to the graph of the function and other methods to solve the equation.  The examples are: x^2 +4x -21 = 0 which is factorable and has two real solutions; 3x^2 +6x +10 = 0, which has no rational roots so cannot be factored using rational numbers — indeed it has no real solutions (the graph doesn’t intersect the x-axis), so the quadratic formula is the best and easiest way to solve this problem; -3x^2 +12x +1 = 0, which has two real solutions.
  2.  \rhd Using the quadratic formula (rearranging) (2:21) Rewrite the equation 6x^2 + 3 = 2x - 6 in standard form and identify a, b, and c.
  3. \rhd Determining the number of solutions to a quadratic using the discriminant (4:58) Example used: x^2 +14x+49 = 0.
  4.  \star Practice determining the number of solutions of a quadratic (including interpreting graphical information)
  5.  \star Practice solving quadratic equations using the quadratic formula.
  6.  \rhd Derivation of the quadratic formula (using completing the square to solve ax^2 + bx+c = 0