 I. Solutions of Quadratic Equation: x-intercepts=solving=finding roots=finding the zeros A. One Real SolutionB. Two Real Solution C. No Real Solution

A. Solve by finding the Square Roots  isolate the term with the variables on one side of the equation.  divide both sides by the coefficient a.  take the square root of both sides.  remember when taking square roots, it is positive and negative value

 1.2.

Think about what happens when you solve this problem: (x+2) 2 In general, the constant term in the perfect square trinomial is the square of _______ the coefficient of the second term.

B. Solving by Completing the Square It is a process by which we can force a quadratic expression to factor. 1. coefficient of the x squared term must equal to 1(if it is not divide everything by it) 2. isolate the terms containing x on the left side of the equation 3. take half of the coefficient of x and square it 4. add this number to both sides of the equation 5. write the left side as the square of the binomial 6. take the square root of both sides. Then solve for x

1.2.

 We know the ROOTS(SOLUTIONS) of a polynomial are its intercepts.  Remember x-intercepts occur where y=0.  The quadratic formula will always work to find the roots/ solution.

Steps to using the Quadratic Formula: 1.Write in standard form: (Set = to zero, like when factoring) 2. Divide by the common multiple, if there is one 3. Identify a, b, and c. Then evaluate. Make sure your radical is simplified.

x 2 =-20x

Did you notice a relationship between the number of solutions and the b 2 -4ac portion of the formula? b 2 - 4ac portion of the formula is called the discriminant If b 2 - 4ac > 0, then there are two x- intercepts(two real solutions) If b 2 - 4ac = 0, then there is one x-intercept(one solution—double root) If b 2 - 4ac < 0, then there are NO x- intercepts(two conjugate imaginary roots) Therefore, it is possible to know how many solutions there will be prior to solving.

 When a quadratic is factorable, the easiest method of solving is by factoring.  1. Set the equation equal to zero.  2. Factor the quadratic.  3. Set each factored piece equal to zero.  4. Solve each factored piece.

1. 12 = - 2x x2. 3x-6=x t 2 -17t+45=3t-5

 Homework:  Worksheet on 6.4, 6.5, and 6.3.