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Algebra I

To take the square root, you need how Many to pull out? Two

Three To take the cube root, you need how Many to pull out?

Add the exponents X to the 9th X to the third times x to the sixth

Multiply the exponents When raising a power to a power ___ the exponents.

In the bottom (denom.) A negative exponent means to place That part of the answer where?

Subtract When dividing polynomials, ____ the exponents.

One Any term raised to the zero Power = ?

Add all sides To find perimeter …

Combine like terms To add polynomials …

1.Change subtraction to addition 2.2.Change 2 nd polynomial to its opposite To subtract polynomials …

Length x width A = lw Area = ?

2 x squared – x - 6 (2x + 3)(x – 2)

GCF When factoring, look for the ____ first.

+ - X divide Sum, Difference Product, Quotient Mean to ____.

X - 6 X squared -2x-24 divided by X+4

X - 4 A rectangle has a width of 2x + 3 and An area of 2x squared – 5x -12. What is the length?

Addition Plus, more than, increased by, Additional, sum are ____ indicators

Multiplication Times, twice, of, product, per are ____ indicators.

Subtraction Less, less than, fewer than, Decreased by, difference are ____ indicators.

Less than Which subtraction word indicators Switch the order?

Division Quotient, share equally, separate into Equal groups are ___ indicators.

Y1=left side Y2=right side Zoom 6, 2 nd calc 5 enter 3 times To solve equations in the calculator: Y1 Y2

Take the square root. The opposite of squaring is to _______

Multiplication Two things side by side with no sign in Middle is what operation?

Rises up and to the right A line that has a positive slope Looks like…

Falls to the right A line that has a negative slope Looks like….

Zero A horizontal line has what slope?

Undefined A vertical line has what slope?

M = y – y / x - x Slope given two points M =

Undefined No slope Slope of (3,0) & (3,2)

Rise / Run Slope is what direction over What direction?

Same slope Parallel lines have what type Of slopes?

Opposite Reciprocal slopes Perpendicular lines have ___ ____ slopes?

- 1 The product of the slopes of Two perpendicular lines is Always ___.

Where the graph crosses or Touches the x axis. X intercept

Where the graph crosses or Touches the y axis. Y intercept

Y = mx + b Slope Intercept Form Equation

Plain number by itself X term is positive No fractions or decimals Standard Form

Stat/enter X #’s into L1,Y #’s into L2 stat => calc,4, enter twice Y=vars 5=>EQ enter 2 nd graph to predict Calc steps for graphing, slope int form Equation, predictions:

Y – Y1 = m ( X – X1) Point Slope Form Equation

Y = The equation of a horizontal Line…

X = The equation of a vertical line …

One solution Consistent Independent system Systems of Equations: Two intersecting lines:

No solution Inconsistent system Systems of Equations: Parallel lines:

Infinitely Many Solutions Consistent Dependent system System of Equations: Only one line: (The two lines coincide)

> < Inequality signs: Greater than Less than Not equal to

Open circles have what type of Circles when graphing?

Closed circles Greater than or equal to, Less than or equal to have what Type of circles when graphing?

If you multiply or divide BOTH Sides by a Negative. When does the inequality sign Reverse?

Left Solve inequalities so that the letter Is on the ___ side.

Transitive Property Three ( =) Three inequalities Two insides are the same: What property?

Broken line Two variable inequalities: What type of line? Greater than or Less than?

Solid Two variable inequalities: Greater than or equal to Less than or equal to have what Type of line?

Y = To graph equations and inequalities In the calculator, Solve for ___ first.

Left of Y1 And left of Y2. To put > or < in the calculator, Go where?

The region with the darker shading Is the solution. When solving inequalities by graphing, Where are the solutions?

Real roots, zeros, x intercepts, Solutions. ___, ___, ___, ___ are all where The graph crosses or touches the X axis.

One real solution How many real solutions does a Quadratic have if it touches the X axis once?

Two real solutions How many real solutions does a Quadratic have if it touches the X axis twice?

No real solutions How many real solutions does a Quadratic have if it does not touch the X axis?

When Y = 0 F(x) = 0 The solutions to solving Quadratic Equations using a table are Y or f(x) = ____ ?

Distributive Addition Property of equality Division Property of Equality Property Justification: -3(2x+5) = 9 Given -6x -15 = 9 ____ -6x=24 ____ X = -4____

If the x coordinates repeat => No If the x coordinates are all different => Yes How do you tell if a relation is A function?

Yes Is y = -5 a function?

No Is x = 3 a function?

Use the vertical line test. Touches once => Yes Touches more than once => No How do you tell if a graph is a Function?

When graphed, it is a straight line. What is a linear function?

Solve for y first and graph. No, it is not a function. Graph x = y squared. Is it a function?

F(x) = 4x - 3 Write an equation to represent the Function: f(x) is 3 less than 4 times the Square of x.

Adding the same number to get The next number. What is an arithmetic sequence?

Common difference The number being added each Time in an arithmetic sequence is The ___.

D = a2 – a1 (second term – first term) How do you find the Common Difference?

A (n) = last term A1 = first term N = # of terms D = # being added A(n) = a1 + (n – 1) d Identify each term.

A(n) = 5n – 7 A (15) = 68 -2,3,8,13,… Write a formula for finding the nth term Find the 15 th term in the sequence.

Domain is the x coordinates. What is the domain of a relation?

The range is the y coordinates. What is the range of a relation?

Range. The y answer depends on the Value of x. Which is the dependent variable Domain or Range?

Domain => -4<x<5 (or equal to) Range => -1<y<5 (or equal to) Describe the domain and range for function(-4,4)(-3,5)(-1,0)(1,-1)(5,3) (Connected)

Domain: all real numbers Range : all real numbers Describe the domain and range for F(x) = 4x -4.

Domain : all real numbers Range: f(x) = 3 or y = 3 Describe the domain and range For f(x) = 3.

Left and right to see how wide it is. To describe the domain of a graph, Stretch which way?

Up and down to see how tall it is. To describe the range, stretch which Way?

Y = kx In direct variation, y is directly proportional to x. Write the formula or equation,

It goes DIRECTLY to and or through The origin. How does a direct variation graph Look?

K = slope Y intercept = (0,0) For a direct variation graph, what is The constant of proportionality? Y intercept?

Y = k/x Write the formula for inverse variation.

x1 over x2 = y1 over y2 (proportion) Direct variation proportion:

X1 over x2 = y2 over y1 Inverse Variation Proportion:

Cross multiply and divide. To solve proportions …

Stat/enter Key #’s into L1 2 nd 0 (down to Mean, 2 nd L1) M.A.D. => Stat=>Calc enter twice How do you find the: Mean: Mean Abs. Dev.

Variance = standard deviation Squared. Variance = ????

Z – score = # - mean/ st. dev Z – score =

Draw a bow-&-whisker plot Box-&-Whisker Plots: identify: lower Extreme, LQ,whisker,median,UQ, Upper extreme

Range = highest # - smallest # IQ = UQ - LQ Range = IQ Range =

Stat/enter #’s into L1 & L2 Y = clear & unhighlight 2 nd y= Enter/On Zoom 9 to graph,stat,calc,5enter 3 times, 2 nd graph to predict To graph quadratics:

2 (2x squared – x – 1) 2 ( 2x+1)(x-1) Factor 4x squared -2x-2.

Inverse for addition Identity of addition Commutative of addition Which property? 10a + -10a = 0 10a + 0 = 10a A+10= 10+a

Associative of addition Distributive Which property? 9x + (3x + 8) = (9x+3x) + 8 8(3x-2) = 24x - 16