# Chapter 5 (Alg 2) Flashcards

1
Q

A

a function that can be written in the standard form y = ax^2 + bx + c were a DNE 0

2
Q

Parabola

A

Graph of a Quadratic formula

3
Q

Axis of Symmetry

A

divides the Parabola into mirror images and passes through the vertex

4
Q

Vertex

A

The lowest or highest point on a parabola

5
Q

Graphing a standard quadratic function

A

Draw axis of symmetry, x = -b/2a
Plot the vertex
Fill in some data values

6
Q

Monomial

A

a number, a variable, or the product of a number and one or more variables with whole number exponents

7
Q

Bi-nomial, Tri-, Poly-

A

the sum of two monomials, three, four or more

8
Q

Vertex form of Quadratic

A

y = a(x-h)^2 + k, h is the axis of symmetry (this is standard for a lot of the equations you’ll come across in the future)

9
Q

Graphing Vertex form of Quadratic

A

Draw axis of symmetry, plot vertex (h,k), plot more data points

10
Q

Intercept form of Quadratic

A

y = (x - p) (x - q)

11
Q

How to graph intercept form of Quadratic

A

Draw axis of symmetry which is p + q over 2, Plot vertex, plot more data points

12
Q

Minimum and Maximum of Quadratic graph

A

a > 0, the y-coordinate of the vertex

a

13
Q

How to factor a Trinomial

A

find integers m and n such that m + n = b and mn = c

(x^2 + bx + c)

14
Q

A

written as ax^2 + bx + c = 0

15
Q

Zero product property

A

Let A and B be expressions, if AB = 0, then A = 0 or B = 0

16
Q

Factor a trinomial ax^2 +…

A

finding numbers k and j whose product is a and numbers mn = c

17
Q

Zeros of a function

A

x-values for which the function’s value is zero, there also the x-intercepts.

18
Q

Differences of Two Squares Pattern

A

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

19
Q

Perfect Square trinomial patterns

A

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

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

20
Q

Square root (definition)

A

If b^2 = a then Sqrt. a = b
A number b is a square root of a number a if b^2 = a
A positive number a has two square roots written Sqrt.a and - Sqrt. a

21
Q

A

the expression Sqrt. a

22
Q

A

Sqrt. sign (not technically)

23
Q

A

the expression under the Radical

24
Q

Properties of Square Roots (Product, Quotient)

A

Sqrt. ab = Sqrt. a times Sqrt. b

Sqrt. (a over b) = Sqrt. a over Sqrt. b

25
Q

Imaginary unit i

A

Defined as a number such that i^2 equals -1, i = Sqrt. -1

26
Q

Complex number

A

(a + bi), a is the real part, bi is the imaginary part
{}
To add or subtract complex numbers, add or subtract their real and their imaginary parts separately

27
Q

Complex Conjugates

A

in the form of a + bi and a - bi, Using the special product rule, multiplying them will result in all real numbers

28
Q

Completing the square

A

adding a constant c to the expression x^2 + bx to make it a perfect square trinomial
{}
x^2 + bx + (b/2)^2 = (x + b/2)^2

29
Q

A

x = (-b + - Sqrt. b^2 -4ac)/ 2a

30
Q

If the Discriminent is >, =,

A

2 real solutions
1 real solution
2 imaginary solutions

31
Q

Vertical Motion Models (Dropped, falling object; Launched or Thrown Object)

A
```h = -16t^2 + h sub 0
h = -16t^2 + v sub 0 t + h sub 0```
32
Q

Rationalizing the denominator

A

Eliminating any radical from the denominator, to simplify

33
Q

The Square root of a negative number

A
```If r is a positive real number, then Sqrt. -r = iSqrt.r
By property (1), it follows that (iSqrt.r)^2 = -r```