2.3 Quadratic Functions, Square Root

part 2

Pgs. 259-265

Objectives F-IF.4, F-IF.8, A-REI.4b

• For a function that models a relationship between two quantities, interpret key features of graphs and tables in terms of the quantities, and sketch graphs showing key features given a verbal description of the relationship. Key features include: intercepts; intervals where the function is increasing, decreasing, positive, or negative; relative maximums and minimums; symmetries; end behavior; and periodicity.*

• Write a function defined by an expression in different but equivalent forms to reveal and explain different properties of the function.

• Solve quadratic equations in one variable.– b. Solve quadratic equations by inspection (e.g., for x2 = 49),

taking square roots, completing the square, the quadratic formula and factoring, as appropriate to the initial form of the equation. Recognize when the quadratic formula gives complex solutions and write them as a ± bi for real numbers a and b.

Perfect Square Trinomial: the product you obtain when you square a binomial. ◦ The first term and the third term of the trinomial

are always positive, as they represent the squares of two terms of the binomial.

◦ The middle term of the trinomial is two times the product of the terms of the binomial

Vocabulary

What??

Difference of Two squares: an expression of the form a2 – b2

Vocabulary

a2 + 2ab + b2 = (a + b)2

a2 - 2ab + b2 = (a – b)2

Factoring Perfect Square Trinomials

Factor 9x2 – 42x + 49

Step 1: Take the square root of the first term and the third term.

Step 2: Put the terms in the parenthesis squared and separate the terms with a plus/minus sign (depending on your second sign).

Example : Factoring a Perfect Square Trinomial

Factor 4x2 + 12x + 9

Example: Factoring a Perfect Square Trinomial

1) Factor 64x2 – 16x + 1

2) Factor 25x2 + 90x + 81

Example: Factoring a Perfect Square Trinomial

a2 – b2 = (a + b)(a – b)

Factoring a Difference of Two Squares

Factor x2 – 4

Step 1: Take the square root of the first term and the third term.

Step 2: Put the terms in two sets of parenthesis, one with a plus sign and one with a minus sign.

Example: Factoring a Difference of Two Squares

Factor 9x2 - 1

Example: Factoring a Difference of Two Squares

1) Factor x2 – 64

2) Factor 4a2 - 49

Example: Factoring a Difference of Two Squares