1. Vocab, Examples, Distributing and Factoring
Quadratics
Vocab, Examples, Distributing and Factoring

2. Vocab
Quadratic fucntion Relationship that compares independent and dependent variables with a power of 2, y=x2 Parabola The graphical representation of a quadratic function

3. Vocab
Term – number, variable or combination of both 2,x,3y Expression – 1 or more terms separated by + or - Monomial – 1 term 2, 3x Binomial – 2 terms x-4, 2x+3 Trinomial – 3 terms Polynomial are all of the above and any that are larger, 4,5,6 terms

4. Quadratic
Factored form usually 2 binomials being multiplied (x-2)(x+3) Expanded form or Standard Everything is distributed, exponent is squared

5. Distributive Property
Multiply the term outside the parenthesis to all terms inside the parenthesis Multiply terms – number to number variable to variable, only exponent on variable changes, number gets written first

6. FOIL
Process used to multiply binomials together, helps you to remember to multiple all terms F(irst)– first term in each binomial O(utside) – two terms farthest away from each other I(nside) – two terms closest to each other L(ast) – last term in each equation Make sure you include the sign when multiplying, sign is the new operation

7. FOIL
Combine like terms

8. Using the Box or Area model
(x+4)(x+5) Square is x by x and then you add rectangles to make the new dimensions Finding the area of a rectangle is length times width Fill in the parts of the BOX – by multiplying what makes the box Combines the values in the boxes to make a quadratic +4 4x 20 X
X^2 5x +5

9. Factor
Undo the distribution What is common in all terms that can be written in front of the parenthesis

10. Factoring a Trinomial Go from a trinomial to 2 binomials
Only looking when leading coefficient is a 1 (this is the number in front of the x square)
Method 1
Find factors of last term that add to coefficient of middle term
Use factors to write binomials
(x factor)(x factor)
Sign of factor is the operation

11. Method 2 The box method ? 9 X X^2 x
We talked about using the box to find the area how would we do that backwards.
Could you fill in the blanks of this to make it true ? 9 X
X^2 x

12. Examples

13. Special Cases to Factor
Perfect Square the trinomial with factor down into one binomial squared Difference of Squares not a trinomial but a binomial that can be factored like a trinomial, this is a special case because when it gets factored the two binomials have the same terms just opposite signs

14. Parabolas
Maximum point – highest point of parabola, where it changes direction, also known as vertex Minimum point – lowest point of the parabola X-intercepts – there are 2 of them, where graph crosses x axis this means that y=0 Y-intercept – there is only 1, where graph crosses y axis this means that x=0, constant term in expanded form Constant term – number that has not variable by it expanded form Line of symmetry – line through vertex or maximum point that gives you a mirror image Vertical Line x = x coordinate of max point are vertex