Unit 5: Quadratic - Garde 9

Question 1

Distributive Law

Answer 1

a(b + c) = ab + ac

Question 2

One term

Answer 2

monomial

Question 3

Two terms

Answer 3

binomial

Question 4

Three terms

Answer 4

trinomial

Question 5

Expanding monomials

Answer 5

• properties of exponents
  a^m x a^n = a^(m+n)

Question 6

Multiplying two binomials

Answer 6

(a + b)(c + d) = ac + ad + bc + bd
FOIL

Question 7

Square of a binomial

Answer 7

(a + b)^2 = (a + b)(a +b) = a x a + a x b + b x a + b x b
a^2 + 2b + b^2

Question 8

Product of conjuagates

Answer 8

(a + b)(a - b) = a^2 - b^2

Question 9

Factoring

Answer 9

1) GCF: greatest common facotr
- it may be constant variable or both.
2x^2 - 8x = 2x(x - 4)
2) DOS: Check for a difference of square
- first a perfect square
- second a perfect square
- minus between two terms
- if so: factor as (root of first + root of second) (root 1 - root 2)
4x^2 - 361 = 2x - 19

*if not, you can not factor it

Question 10

Factorizing expressions with four terms

Answer 10

Grouping them in two pairs
- ax^2 + ax + 2x + 2
= ax(x + 1) + 2 (x + 1) {factorising each pair}
= (x + 1)(ax + 2) {(x + 1) is a common factor}

Question 11

Quadratic trinomial facorization

Answer 11

ax^2 + bx + c
- x is a variable
- a, b, c are common constants, a is not equal to 0
(x + 1)(x +6)
x^2 + x + 6x + 6
x^2 + 7x + 6
x^2 + (p + q)x + pq
- the coefficient of x is the sum of p and q
- the constant term is the product of p and q
(x + p)(x +q)

Question 12

Function Notation

Answer 12

linear function:
y = mx + b (x-y notation)
f(x) = mx + b (function notation)
f(x) is “f of x”

Question 13

Quadratic function

Answer 13

f(x) = ax^2 + bx + c
Parabolas
-a: concave down
a: concave up
a is the “leading” coefficient
c: y-intercept
b: coefficiant
axis of symmetry: x = x-intercept of vertex
f(x), x are variables

Question 14

Vertex

Answer 14

minimum or maximum value on a parabola

Question 15

Quadratic term

Answer 15

ax^2

Question 16

Linear term

Answer 16

bx

Question 17

Constant term

Answer 17

c

Question 18

Method 2 of factoring quadratic trinomials

Answer 18

6x^2 - 7x -10
- multiply a and c
6x^2 x 10 = -60x^2
- find two factors of -60 that up to -7
-12x and 5x
- Replace bx (7x) with these factors
6x^2 - 12x + 5x -10
- then simplify
6x(x - 2) + 5(x - 2)
(6x + 5)(x - 2)

Question 19

x-intercept of a function, f(x)

Answer 19

are also called the “zeros”

Question 20

Factored form

Answer 20

y = a(x - p)(x - q), a does not equal zero
- axis of symmetry: (p + q)/2
- p and q are x-intercepts

Question 21

Standard form

Answer 21

y = ax^2 + bx + c
axis of symmetry: -b/2a
vertex: -b/2a, f(-b/2a)

Question 22

Vertex form

Answer 22

y = a(x - h)^2 + k, a does not equal zero
- (h, k) are the vertex

Question 23

Factored to Standard form

Answer 23

look in book

Question 24

Standard to vertex form

Answer 24

(b/2)^2 to find the number needed to add and subtract from both sides
- factor from there and find k

Question 25

Function

Answer 25

A set of ordered pairs in which each first coordinate corresponds to a distinct second coordinate (no vertical points in a function)

Question 26

Vertical line test (VLT)

Answer 26

used to determine if the given graph represents a function
Ex: if a vertical line intersects the line more than once, it does not represent a function.

Question 27

Domain

Answer 27

the area x can occupy from a line, parabola or circle

Question 28

Range

Answer 28

the area y can occupy from a line, parabola or circle

Question 29

Zero product theory (null factor law)

Answer 29

• if a x b = 0, then a = 0 or b = 0
  ax^2 + bx + c
  Solutions are x-intercepts of the graph.
  To factor:
• terms of LHS (leave zero on RHS)
• Simplify: combine terms
• Factor LHS
• Apply zero product theorem