Chapter 5 (Alg 2)

Question 1

Quadratic Function

Answer 1

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

Question 2

Parabola

Answer 2

Graph of a Quadratic formula

Question 3

Axis of Symmetry

Answer 3

divides the Parabola into mirror images and passes through the vertex

Question 4

Vertex

Answer 4

The lowest or highest point on a parabola

Question 5

Graphing a standard quadratic function

Answer 5

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

Question 6

Monomial

Answer 6

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

Question 7

Bi-nomial, Tri-, Poly-

Answer 7

the sum of two monomials, three, four or more

Question 8

Vertex form of Quadratic

Answer 8

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)

Question 9

Graphing Vertex form of Quadratic

Answer 9

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

Question 10

Intercept form of Quadratic

Answer 10

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

Question 11

How to graph intercept form of Quadratic

Answer 11

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

Question 12

Minimum and Maximum of Quadratic graph

Answer 12

a > 0, the y-coordinate of the vertex

a

Question 13

How to factor a Trinomial

Answer 13

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

(x^2 + bx + c)

Question 14

Quadratic equation

Answer 14

written as ax^2 + bx + c = 0

Question 15

Zero product property

Answer 15

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

Question 16

Factor a trinomial ax^2 +…

Answer 16

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

Question 17

Zeros of a function

Answer 17

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

Question 18

Differences of Two Squares Pattern

Answer 18

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

Question 19

Perfect Square trinomial patterns

Answer 19

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

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

Question 20

Square root (definition)

Answer 20

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

Question 21

Radical

Answer 21

the expression Sqrt. a

Question 22

Radical Sign

Answer 22

Sqrt. sign (not technically)

Question 23

Radicand

Answer 23

the expression under the Radical

Question 24

Properties of Square Roots (Product, Quotient)

Answer 24

Sqrt. ab = Sqrt. a times Sqrt. b

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

Question 25

Imaginary unit i

Answer 25

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

Question 26

Complex number

Answer 26

(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

Question 27

Complex Conjugates

Answer 27

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

Question 28

Completing the square

Answer 28

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

Question 29

Quadratic Formuala

Answer 29

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

Question 30

If the Discriminent is >, =,

Answer 30

2 real solutions 1 real solution 2 imaginary solutions

Question 31

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

Answer 31

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

Question 32

Rationalizing the denominator

Answer 32

Eliminating any radical from the denominator, to simplify

Question 33

The Square root of a negative number

Answer 33

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