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Unit 10: Quadratic Functions

Unit 10: Quadratic Functions. 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!

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Unit 10: Quadratic Functions

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  1. Unit 10: Quadratic Functions Topic: Solving Quadratics by Factoring & Square Roots

  2. 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).

  3. 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.

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

  5. 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.

  6. 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.

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

  8. 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.

  9. 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

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

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