Algebra 1 Staar Review - Basics

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Multiply across parenthesis.

Don't forget to distribute negative.

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The number multiplied by variables.

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A polynomial with 3 terms.

Terms are separated by + or -.

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A polynomial with 2 terms.

Terms are separated by + or -.

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Equations include an = sign.

Expressions have NO = sign.

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General steps:

1) Distribute

2) Combine Like Terms

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Terms are separated by + or -.

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Left Hand, Less Than.

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Greater Than

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( x , y )

( Left/Right , Up/Down)

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The phrase "less than" tells us to reverse the order.

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The phrase "more than" tells us to reverse the order.

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If a Vertical Line touches/crosses the graph more than once, it is NOT a FUNCTION.

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When you multiply or divide by a NEGATIVE, FLIP the inequality symbol.

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Vertical lines have an equation x = #.

Vertical lines have Undefined Slope.

VUX (Vertical, Undefined, x=)

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Horizontal lines have equation y = #.

Horizontal lines have slope = 0.

HOY (Horizontal, ZerO, y=)

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Combine Like Terms by adding Coefficients of Like Terms.

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Half means to:

-Divide by 2

OR

-Multiply by 1/2

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Quotient means to DIVIDE.

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Difference means to SUBTRACT.

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Sum and Total BOTH mean to ADD.

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Product means to MULTIPLY.

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IS and WAS both generally mean EQUALS.

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Twice means Double or to Muliply by 2.

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Negative Parabola

- opens down

- 'a' value is negative

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Positive Parabola

- opens up

- 'a' value is positive

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Axis of Symmetry (Line of Symmetry)

- passes through the Vertex

- passes through the x-axis

- splits the parabola in half

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ROXS

R - Roots

0 - zerOs

X - x-intercept

S - Solution

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Vertex

- minimum or maximum of parabola

- highest or lowest point on graph

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Finds solutions for quadratics.

Remember song "Pop Goes the Weasel"

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Exponent is the superscript.

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For exponents, expand the expression

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Squared means to the power of 2.

Often referring to area.

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Cubed means to the power of 3.

Often referring to volume.

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When multiplying powers (with the same bases), ADD exponents.

OR

Expand and add up. (Don't forget to multiply coefficients)

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When dividing powers (with same bases), SUBTRACT exponents.

OR

Expand and cancel out. (Don't forget to divide coefficients)

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When there is an exponent outside the parenthesis, multiply exponents.

OR

Repeat parenthesis.

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Negative exponents cannot be left negative, they must be moved.

If the neg exp is in top - move to bottom (and remove neg)

If the neg exp is in bottom - move to top (and remove neg)

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Anything to the power of 0 = 1

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Domain:

- x values

- bottom to top

Range:

- y values

- left to right

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Domain:

- x values

- input

- cause

- independent variable

Range:

- y values

- output

- effect

- dependent variable

- effect

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Parallel lines have the same slope and the lines never touch.

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Perpendicular lines create a right angle (90 degress).

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X-intercept:

-where the line crosses the x-axis

-( x , 0 )

-known as 'zero' for linear fcts

-known as 'ROXS' for quadratics

y-intercept:

-where the line crosses the y-axis

-( 0 , y )

-known as 'b' in linear fcts

-known as 'c' for quadratics

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Point Slope Formula

-solve for y

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Linear Functions create a straight line

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y = mx + b

-m represents slope

-b represents y-int

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To find slope from a graph use

rise over run

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m - represents slope

b - represents y-int

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slope is rise over run

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horizontal lines have zero slope (m = 0)

HOY (horizontal, m=0, eqn y=#)

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Vertical lines have Undefined slope (sometimes called No Slope)

VUX (vertical, Undefined, eqn x=#)

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a linear graph goes down (from left to right) when the slope is negative

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the solution to a system (more than one equation together) is the point the two lines have in common

or the intersection

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The solution to a system is the POINT (x,y) where the two lines intersect

or the point the two lines have in common

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Slope Intercept Form

m - slope

b - y-intercept