Factored Form to Standard Form
Recall: Factored Form: y=a(x­s)(x­t)
Standard Form: y=ax2+bx+c
To convert the equation of a quadratic relation from factored form to standard form, we will expand, regroup, then simplify the factored form.
ex. Rewrite y=(x+2)(x+1) in standard form.
Method 1: We will use algebra tiles. Think of this like a room with
dimensions (x+2) by (x+1). The area of the room is (x+2)(x+1). We are
trying to determine another way of expressing the area.
x
x
x
1
2
x
1
x
1
1
x
1
Method 2: Mock algebra tiles
The area of the
room is...
Method 3: Algebraic Ungrouping
y=(x+2)(x+1)
Method 4: "FOIL" ‐ make sure each term in one bracket gets
multiplied by each term in the other bracket.
Ex. Express y=(x­2)(x+1) in standard form.
Method 1: Algebra Tiles
x
x
1
x
2
x
red blocks are negative
1
1
x
x
1
1
Method 2: Mock Algebra Tiles
Method 3: Algebraic Manipulation
Method 4: "FOIL"
1
Work on the following questions with the person beside you. 10 minutes
pg. 288 #1 ad
#2 bc
#3
#4 bf ­­ verify using an algebraic method. Check your answers:
pg. 288 #1 a (x+2)(x+1) = x2 +3x + 2
d (2x+2)(x+2) = 2x2 + 6x + 4
#2 b 2x2 + 7x +6
c x2 ­ x ­6
#3 (no specific answer, here is a suggestion)
You distribute each term of one binomial by multiplying it by each term in the other binomial. Since there are two terms in a binomial, you distribute twice.
#4 b 2x2 + 5x + 2
f 6x2 + x ­1
Ex. Rewrite the following in standard form:
Use any method.
a) y=3(x­1)(x­5)
Answer:
b) y=(2x­1)(3x+4)
Answer:
2
Ex. Determine the equation of this parabola, in standard form.
convert to standard form
by expanding
Ex. The point (­3,­4) lies on the parabola which has zeroes at ­1 and ­5. Determine the equation of this parabola in standard form.
expand from factored form to
standard form
3
challenge
HW: p. 298 # 2ad, 3agj, 5ag, 7a, 8bd, 9a, 10ce 4
Attachments
Algebra Tiles.xbk