March 8 Quadratic Equations

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March 8 Quadratic Equations

  1. 1. Quadratic Equations
  2. 2. Vocabulary recap Monomial = 1 term i.e. 3, 4x, x 2y Binomial = 2 terms that cannot be combined i.e. n + 3, 4x 2+y Trinomial = 3 terms that cannot be combined 2 3 5 i.e. x + 3x + 5, y + 5x - x
  3. 3. Polynomial = any number of terms that cannot be combined i.e. any monomial/binomial/trinomial or bigger Quadratic = a polynomial of the form 2 ax + bx + c = 0, can be graphed to form a parabola.
  4. 4. Given (a)(b) = 0 if nothing else is known what conclusions can be drawn from the above? it is true if a or b = 0 0(b) = 0 (a)0 = 0 so we know that a or b must be 0, or both.
  5. 5. given a function 2 f(x) = ax + bx + c the roots, aka the zeros, aka the x intercepts are the values of x when the f(x) is 0. Put another way where y = 0
  6. 6. f(x) = x 2 + 5x + 6 Find the roots of the function The roots are when f(x) =0 so 0 = x2 + 5x + 6 0 = (x+2)(x+3) 0=x+2 0=x+3 x = -2, -3
  7. 7. So if we wanted to graph the previous function we know the parabola intercepts the x axis at -2 and -3
  8. 8. Exercise 13 Bonus: solve for x ax 2 + bx + c = 0 hint: you'll need to complete the square!

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