Download Unit 2 Vocab and Notes

Math II Chapter 1 Vocabulary & Notes

Vertex is the highest or lowest point. It is written as a coordinate pair; for example (2,3)

Axis of Symmetry is the line that divides the parabola in half (left to right) and creates a
mirror image.
The Axis of Symmetry will be the X value of the Vertex.
The Axis of Symmetry is always written as X = ____.
For example, if the Vertex is (2,3), the Axis of Symmetry is X = 2

Zeros are the X-intercepts or where the parabola crosses the X axis. The zeros are written
as a coordinate pair where the y value will always be zero

X-intercept is where the parabola crosses the X-axis. Put zero in for Y value then solve for
the X value.
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Y-intercept is where the parabola crosses the Y-axis. Put a zero in for the X value and solve
to find the value for Y.

Parabola is a U-shaped graph of a quadratic equation. The parent function is f(x)= X2.

Quadratic equation is f(x)= ax2 + bx + c or f(x)= a(x – h)2 + k

Domain is the collection/ set of X-values
For a quadratic function, the domain is always “All Real Numbers” or
.

Range is the collection/ set of Y-values.
For a quadratic function, the range will either be ≥ or ≤ that y value of the vertex.

If a is positive in f(x)= ax2 + bx + c the vertex is the lowest point and the y-values are
decreasing on the left side of the vertex and increasing on the right side of the vertex.

If a is negative in f(x)= ax2 + bx + c the vertex is the highest point and the y-values are
increasing on the left side of the vertex and decreasing on the right side of the vertex.

Read graphs Left to Right (like reading a book)

Extreme points or Extrema is the maximum or minimum point on a graph (e.g., the
vertex)

Interval notation: Open interval (a, b) is all numbers between a and b, but does not
include a or b

Interval notation: Closed interval [a, b] is all numbers between a and b and also includes
a and b.

Interval notation: Half-closed/ half-open interval. The interval includes the number on
the side with the brackets, with the parenthesis does not include the number.
[a, b) = numbers between a and b, including a but not including b
(5, 10] = numbers between 5 and 10, including 10 but not 5
[0, ∞) = the set of numbers greater than and equal to zero

To factor quadratic equations use the area model.

Standard form is ax2 + bx + c = y

If you are given an X coordinate of a vertex, plug that value into the equation to get your Y
coordinate

The X coordinate of the vertex = -b/ (2a)

The Y coordinate of the vertex = f(-b/2a) (Plug the x value in and solve!)

In Standard Form, when a < 0, the vertex is the highest point of the parabola (the parabola
opens down).

In Standard Form, when a > 0, the vertex is the lowest point of the parabola (the parabola
opens up).

Vertex form: f(x) = a(x-h)2 + k where your vertex is (h, k)

Converting from Vertex Form to Standard Form:
a(x-h)2 + k =0
a(x-h)(x-h) + k = 0
You have to FOIL the (x-h)2 terms

When graphing a parabola, find the vertex and then pick two x values greater and two x
values less than the x value of the vertex.
Math II Chapter 2 Notes & Vocabulary
The Quadratic Formula gives you the roots/ zeros/ x-intercepts/ solutions (remember these are all the same
thing) of a quadratic formula.
 b  b 2  4ac
The Quadratic Formula is x 
2a
Roots/ Solutions are written as x = ____ (what you find when you solve the Quadtratic Formula)
Zeros are written as a coordinate pair with the x-value as whatever you find when you solve the Quad
Formula and the y-value as 0. (___, 0)
The Discriminant is b2 -4ac
The Discriminant tells you the number and the nature of and the number of the roots of the Quadratic
Functions.
When b2 -4ac < 0  no real roots
When b2 -4ac = 0  one real root
When b2 -4ac > 0  two real roots
Finding the Vertex (written as a coordinate pair) of a parabola:
The x-value of the coordinate pair =
b
; The y-value is found by plugging in your x-value and solving.
2a
Complex Numbers:
Standard form is a + bi where a is a real number and bi is an imaginary term
i  1
i 2  1
Simplifying negative square roots:
For example:
 80   1  80   1 * 16 * 5 
4i 5
Adding & Subtracting Complex Numbers:
Combine like terms (Combine real numbers and then combine imaginary numbers)
For example (3 + 2i) – (1 + 6i) = 3 -1 + 2i -6i = 2 -4i
Multiplying Complex Numbers:
FOIL or Distribute (Depending on your problem) and then simplify!
For example (3 + 2i)(1 + 6i) = 3 + 18i + 2i + 12i2 = 3 + 20i + (12*-1) = -9 + 20i
Dividing Complex Numbers:
Multiply by the Conjugate and then simplify.
Remember the Conjugate is simply the complex number with the opposite sign (For example the conjugate of
(2 + 7i) is (2 – 7i)
Example of Dividing:
1 6i
(1 6i ) (8 3i )
(8 3i  48i  18i 2 )
(8 51i  18) (10 51i)

*



2
8  3i (8  3i ) (8 3i ) (64 24i  24i  9i )
(64  9)
73
Multiplying Conjugate Shortcut
(8 – 3i)(8 + 3i)
Square the first number, Square the second number, and add them together
82 = 64
32 = 9
64 + 9 = 73
The Quadratic Formula with imaginary numbers:
When you work the Quadratic Formula and
on the outside of the
b2  4ac gives you a negative square root, simplify, putting the i
. These are roots, but they are imaginary roots, not real roots.
Solving Quadratic Inequalities
Example: x2 -4x – 2 > -5
1. Set the equation equal to zero.
X2 – 4x -2 +5 > -5 + 5
x2 – 4x + 3 > 0
X2 – 4x + 3 = 0
2. Calculate the zeros/ solutions of the function.
(x – 3)(x – 1)
X = 3 and X = 1
3. Roughly sketch the parabola
4. Find the y-values on the graph that correspond
to the inequality.
(Substitute y in for the equation)
x2 – 4x + 3 > 0
y>0
Y values
greater than 0
5. Decide which values of x will give you these y
values.
x < 1 and x >3
Sequence  List of numbers
Arithmetic Sequence  List of numbers with a particular pattern (e.g., add 2 each time)
Term  A number in a sequence
Common Difference (d)  How much you add or subtract to each term in an arithmetic sequence
Explicit form 
a n  dn a0 ; This gives you a particular term in an arithmetic sequence by
plugging that number (e.g. 20 to find the 20th term) for n
Arithmetic Series  Adding the terms of a arithmetic sequence together
Gauss’s Formula for
finding sum 
Sn 
n(a1  an )
, where a1 is your first term and an is your last term
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