Topic: Solving Quadratics by Factoring & Square Roots

Definitions Zeros of a quadratic function Solutions of a quadratic function Roots of a quadratic function All three refer to the same thing! The value(s) of x that make y = 0 (x-intercepts of the parabola).

How can you solve a quadratic equation without graphing it? Set the equation equal to zero & factor it. Use the Zero Product Property to determine the solutions from your factors. Zero Product Property: If ab = 0, then either a = 0 or b = 0.

Solving Quadratics by Factoring Find factors of ac whose sum is b. Factor using your preferred method. Ms. Bonilla MethodGroup & Factor Method If you use the Punnett Square, the 4 terms from Group & Factor go in the square.

Solving Quadratics by Factoring Use Zero Product Property to find solutions for x. For the statement to be true, either x + 3 =0 or 3x – 2 = 0. Solve each of those for x.

Solving Quadratics by Factoring Set the equation equal to 0 (move 4x to the other side.) Since there is no c, this can’t be factored as a regular quadratic. All we can do is factor out a GCF. Use Zero Product Property to solve for x.

 Square roots can be used to solve quadratic equations when b = 0.  REMEMBER: Square roots actually have two solutions, one + & one -. Example: Solving Quadratics by Square Roots

Divide both sides by a (leave the result as a fraction!). Take the square root of both sides (Remember that a square root distributes to a fraction just like an exponent). This is why we leave the fraction; both numerator & denominator are perfect squares. Solving Quadratics by Square Roots

Journal Entry TITLE: Solving Quadratics CYK Things I Already Knew: Identify at least 2 New Things I Learned: Identify at least 2 Questions I Still Have: Identify at least 2

Quest: Solving Quadratics by Factoring & Square Roots Due 5/18