Quadratics

• Put some words in here toact as a title
• Standard form
  • y = ax² + bx + c

    • coefficient a = 1+, parabola narrows

      a = 0+ to 1-, parabola widens

      a negative, parabola opens downwards

  • y = 2x² + 3x + 6
• Factored form
  • (x + m)(x + n)
    • x² + (m + n)x + mn
  • Build factor tree of c
    • c = mn
  • Factors sum to b
    • b = m + n
  • x² + 5x + 6
    • =(x + 2)(x + 3)
      • 6 = 2 x 3
      • 5 = 2 + 3
• Perfect square trinomial
  • ax² + bx + c

    = (x + ^b/₂)²

    • c = (^b/₂)²
  • x² + 10 x +25
    • =(x + 5)²
  • = square of a binomial
• Vertex form
  • a(x − h)² + k
  • Vertex = (h, k)
  • Completing the square
• Words
  • Monomial
    • Expression/polynomial with

      one term

      • 2x, y, xy, 5
  • Binomial
    • Two terms
      • (x + 3), x² + 4x, 3x³ +4
  • Trinomial
    • Three terms
      • 2x² + 3x + 4
  • Polynomial
    • Many terms
  • Vertex
• Before you start,

  you need to understand...

  • Exponents
  • Functions
  • The Distributive Property
  • FOIL + grid multiplication
  • How to plot a graph
  • Coordinates on

    a coordinate plane

• Solving

  quadratics

  • ax² + bx + c = 0
    • The value/s of x that

      make/s the quadratic = 0

      • Solutions
      • Zeros
      • Roots
      • x-intercepts on a graph
  • Factoring
    • 2x² − 4x − 30 = 0
    • 2(x² − 2x − 15) = 0
      • −15 = (−5) x 3
      • −2 = −5 + 3
    • 2(x − 5)(x + 3) = 0
    • Solutions: x = 5 or −3
  • Completing the square

    • 2x² − 4x − 30 = 0

      2(x² − 2x − 15) = 0

      2(x − 1)² − 32 = 0

      2(x − 1)² = 32

      (x − 1)² = 16

      (x − 1) = ± 4

      x = 1 ± 4

      x = 5 or −3

  • ~ Quadratic Formula