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Quadratics

Quadratics. Factoring. To solve a quadratic equation it must be equal to zero And the terms must be in order!! Use the HAVE – USE Chart sign in the problem signs in the (). Example. SOLVE x 2 – 2x – 8 = 0 Have - and - use + - (x – 4)(x + 2) = 0

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Quadratics

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  1. Quadratics

  2. Factoring • To solve a quadratic equation it must be equal to zero • And the terms must be in order!! • Use the HAVE – USE Chart sign in the problem signs in the ()

  3. Example • SOLVE • x2 – 2x – 8 = 0 Have - and - use + - • (x – 4)(x + 2) = 0 Find the factors of 8 that subtract to give you 2 • (x – 4) = 0 (x + 2) = 0 Set each one equal to zero and solve • x = 4 x = -2

  4. Quadratic Formula If you aren’t comfortable factoring, use the quadratic formula

  5. Example • x2 – 2x – 8 = 0 • A = 1 B = - 2 C = -8

  6. Solving from the answers • If all else fails substitute the possible answers from the multiple choice answers and determine which set of answers makes the equation true.

  7. Translations

  8. General form y = a func(bx – c) + d impacts width impacts movement neg means +/- +/- it is inverted left/right up/down |a| < 1 wide |a| >1 narrow

  9. Example • Basic shape • y = x2 • Translated shape • y = 2(x-1)2 + 3 • y = 2(x-1)2 + 3 • y = 2(x-1)2 + 3 • y = 2(x-1)2 + 3

  10. Graph Recognition

  11. y = x y = x2 y = 1/x • y = x3 y = √x y = 1/x2 • y = log x y = ax

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