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Quadratics
A quick overview
What is a Quadratic?




MUST HAVE
THE x^2 piece!   PARABOLAS!
Factoring

 6          Basically, you are dividing a
            number or expression into parts
            that multiply together to equal it.
2 3
  *




So we will factor quadratic expressions
like: x 2 + 5x + 4 into two factors that
will be equal to it when multiplied
together.
Factor: x^2 + 5x + 4
Play the number game:
What two numbers multiply to give you “c” and add to
give you “b”?




(x          + 4   )(x             + 1)
FOIL to check!
(x +1) (x + 4)

X^2 + 4x + 1x + 4

 x^2 + 5x + 4

Factoring with a = 1
    A little trickier… 2x^2 + 5x + 3
    USE Box Method!
Factors           Factors           Your goal:
of “a”            of “c”
                                    To multiply diaganol numbers and
          2   3                     add them to get “b”



          1   1             (2)(1) = 2 (3)(1) = 3
                            2 + 3 = 5 ! So this works!


                    Write factors like this:

                    (2x + 3) (1x + 1)
Quadratics

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Quadratics

  • 2. What is a Quadratic? MUST HAVE THE x^2 piece! PARABOLAS!
  • 3. Factoring 6 Basically, you are dividing a number or expression into parts that multiply together to equal it. 2 3 * So we will factor quadratic expressions like: x 2 + 5x + 4 into two factors that will be equal to it when multiplied together.
  • 4. Factor: x^2 + 5x + 4 Play the number game: What two numbers multiply to give you “c” and add to give you “b”? (x + 4 )(x + 1)
  • 5. FOIL to check! (x +1) (x + 4) X^2 + 4x + 1x + 4 x^2 + 5x + 4 
  • 6. Factoring with a = 1 A little trickier… 2x^2 + 5x + 3 USE Box Method! Factors Factors Your goal: of “a” of “c” To multiply diaganol numbers and 2 3 add them to get “b” 1 1 (2)(1) = 2 (3)(1) = 3 2 + 3 = 5 ! So this works! Write factors like this: (2x + 3) (1x + 1)