EOC Review by Katherine Franchi

Solve Quadratic word problems

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Practice decoding word problems.

Words for addition: Sum, gain,sum of, plus, Increased by, raised, and enlargement

Words for subtraction: Difference of, less, decrease, take away, deduct, fewer (than), GCF, minus, and withdraw

Words for multiplication: product, of, double, triple, quadruple, as much, per, time, by, and distribute

Words for division: Half of, quotient of, goes into, equal parts, ratio, and divided by

(know words for powers, equals, consecutive integers, and odds)

circle, highlight or box any word you find important in the problem if you prefer too.

STEP 1
Decode word problem.
STEP 2
Write out word problem
Ex. X^2 - 9X = 36
STEP 3
make sure the equation is equal to zero.
Ex.

See if you can simplify the equation down.

Solving By Factoring

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Set all equations equal to zero before beginning
Step 1: Factor Away!
Step 2: Set each factor
Step 3: Solve for X

Formulas

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Y=Mx+b

Exponential Form: y= a(b)^x+k

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mononomial

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only one term

solving systems by graphing

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one solution
infinitely many solutions
no solution

Applications of linear systems

Relation

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A set of ordered pairs

binomial

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two terms

Exponential growth: development at increasingly rapid rate in proportion to the growing total number or size.

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parallel lines

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have no solution

Degree

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Determined by the largest exponent

trinomial

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three terms

Standard Form of a Quadratic Function

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standard form= ax² + bx + c = 0 First find the y intercept by making the value of x zero and use c as the y-intercept.
Next use the Axis of symmetry equation to find x. x = -b/2a
To find the vertex just plug the x you found into the original equation and write the vertex as an ordered pair. (x,y)

Domain- X Values

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Standard Form

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A polynomial in standard form is when exponents are in decreasing order

Exponential Decay: y=a(1-r)^t

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polynomial

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has more than 3 terms

Range- Y Values

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Unit 4: Statistics add

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Frequency: The number of data values in an interval

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linear equations

Vertical line Test

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If you draw a vertical line two points can not fall on the same line.

Vocab

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Mean: The Average for a set of data
Median: The middle value for a data set listed in order
Mode: The most frequently occurring values
Range: The difference between the highest and lowest numbers
Standard deviation: The average deviation of each observation from the mean
Outlier: The value that is extremely different from the rest

Function

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a relationship or expression involving one or more variables.

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Frequency Table: Groups a set of data values and into intervals and shows the frequency for each table

midpoint formula

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Subtraction:

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Step one- distribute the invisible one in front the 1st set of parenthesis
Step two-distribute the invisible -1 to the 2nd set of parenthesis
Step three-combine like terms

Slope

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when the rate of change is constant

FOIL

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F-first:multiply the FIRST two terms
O-outside:multiply the two OUTSIDE terms
I-inside:multiply the two INSIDE terms
L-last:multiply the LAST two terms

In Exponential Growth and Decay Formula, the...

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y=the new amount
a= initial amount
r= rate or decimal
t= time

Standard Form

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answer in an ordered pair

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*Frequency tables do not overlap, do not have gaps, and are usually of equal size

solid lines mean greater/ less than or equal to

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GCF (Greatest common factor)

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Factor: A number or quantity that when multiplied with another produces a given number

30a^5/30a^5 = 30

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dotted lines mean just greater/ less than

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y=mx + b

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Histogram: A graph that can display data from a frequency table

another video

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midpoint forumla: working backwards

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when u r only given the midpoint and u need to find the endpoint, use these steps
1. double the midpoint
2. combine the midpoint and endpoint using the opposite operation of the end pont

Intercept

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Where the line crosses the axis

If there isn't a variable already isolated then you must choose one to solve for, always choose the variable that has a coefficient of 1

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Cumulative Frequency Tables: Shows the number of values that lie in or below a given interval

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Exponential Growth:

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y= a(1+r)^t

can solve by graphing,substitution and elimination

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12^4*12^3 = 12^7

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Setting Up System Of Equations

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How to factor a trinomal in the form of ax^2+bx+c=f(x)

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Step one: factor out the GCF
step two:rewrite the trinomial as a polynomial by slitting the middle term by using the the sides of the X as coefficients.
step three:draw a line between the middle of the two terms to group the polynomial into two parts
step four:Factor out the GCF of each group and write what's leftover inside parenthesis.
step five: write out the coefficients as one binomial and the insides as another binomial.

Sequence

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an ordered list of numbers that form a pattern

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How to factor a Trinomial in the form ax^2 + bx + c

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Step 1: Label your terms with "a", "b", "c"
Step 2: Set up your X
Step 3: See what two numbers multiply to "ac" and add to "b"
Step 4: Take the two numbers and create two binomials
Step 5: Check your answers by FOILing or boxing!

Arithmetic sequence

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a sequence in which the difference between two consecutive terms is constant

Box and Whisker Plot

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independent variable

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does not depend on anything

Distance Formula

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recursive

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based on the previous term

Parallel and Perpendicular

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Parallel Lines- two lines that never intersect and have the same slope but different intercepts

Perpendicular- intersect at 90 degrees angles and have opposite reciprocal slopes

Pythagorean therem

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prime

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a number that can only be divided evenly by one or itself

dependent variabe

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does depend in another variable

Histogram

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Factoring

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factoring is like dividing or using the distributive property backwards

determining if a triangle is right

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step 1- determine the longest side and set that equal to ''c''
step 2- set pyth. ther. with the 2 shortest sides as ''a'' and ''b'''
step 3- determine if the 2 sides of the equation are equal
--> if they are equal, then you have a right triangle
--> if they are not equal, then you do not have a right triangle

scatter plot

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a graph that relates two different sets of data by displaying them as a ordered pair

simplifying radicals

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step 1: factor the number
step 2: rewrite under the radical
step 3: circle like terms (circle the same amount of like terms as the number of the index)
step 4: simplify

Quartile

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Each of four equal groups into which a population can be divided

Legs of a triangle

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The two shorter sides of a triangle

line of best fit

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a line on a scatter plot, drawn near the points, that shows a correlation.

correlation

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a relation or connection between two things

The Quadratic Formula

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x = (-b ± √b²-4ac) / 2a

https://www.youtube.com/ watch?v=U3Qok43VmYg

How to create a Line of Best Fit in the calculator

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Clear your calculator ( 2nd - Plus- 7,1,2)
STAT-Enter
Enter data into L1 and L2
STAT-CALC-4-Enter
substitute the values of "a" and "b" into the Equation "y=ax+b"

3 Methods Of Solving Systems

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Linear:

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progressing from one stage to another in a single series of steps; sequential

Solution possibilities

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In intersecting regions the overlapping shaded region is the solution

Finding GCF

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1.see what they all have in common (including # and variables)
2.remove what is in common
3.divide each term by the GCF and what remains is in the parentheses
4.check by redistributing what you removed

Linear Example:

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Exponential form

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a = y-int. or starting point
b= growth or decay factor
Growth: above 1
Decay: Below 1
Key point (y-int.): (0, a+k)

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slope formula

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slope= rise/run

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Interquartile Range

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Is a measure of variability based on dividing a data set into quartiles

You can tell if it is growth or decay...

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If the b is above 1, it is growth
If the b is below 1, it is decay

Example

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]6

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Positive correlation

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When one thing goes up, the other goes up as well.

Negative Corralation

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a relationship between two variables in which one variable increases as the other decreases.

multiplying monomials with other polynomials

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Distribute first, then combine "like terms" (same variable, same exponents).

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causation

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one thing will cause the other to happen
* correlation does not imply Causation

Trend Line

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A line on a scatter plot, drawn near the points, that shows a correlation

Residual

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The difference between the observed y-value and the predicted y-value (observed - predicted)

Extrapolation

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predicting a value outside the range of known values