Algebra I Flashcards Review

Questions and Answers

What are the x and y intercepts of the equation y = 2x + 4?

X intercept: (-2,0), Y intercept: (0,4)

What is a variable?

A letter that replaces an unknown quantity.

What is a constant?

A number by itself in an expression (no letter with it).

What is a coefficient?

A number multiplied by a variable (the 3 in 3x). Signup and view all the answers

What are the calculator keystrokes for changing a decimal to a fraction or for reducing a fraction?

Math, 1: Frac enter, enter Signup and view all the answers

What must you use when substituting in numbers for variables?

Parentheses Signup and view all the answers

Are negative signs and subtraction signs interchangeable on the calculator?

False Signup and view all the answers

What operation is used for 'quotient'?

Division Signup and view all the answers

What operation is used for 'difference'?

Subtraction Signup and view all the answers

What operation is used for 'product'?

Multiplication Signup and view all the answers

What do you do when evaluating an expression that has a long fraction bar?

<ol> <li>Solve the top, 2. Solve the bottom, 3. Then divide</li> </ol> Signup and view all the answers

How do you enter an exponent in the calculator?

^ 'insert / carrot key' Signup and view all the answers

What is any non-zero number raised to the zero power?

One Signup and view all the answers

What are the steps for simplifying expressions?

<ol> <li>Distribute (multiply to get rid of parentheses), 2. Combine like terms</li> </ol> Signup and view all the answers

What is the order of operations?

Parentheses or Grouping, Exponents, Multiplication/Division from left to right, Addition/Subtraction from left to right Signup and view all the answers

What two things must be the same to combine like terms?

Variable and exponents Signup and view all the answers

What operation do we use to combine like terms?

Addition Signup and view all the answers

If there is a variable with no number in front, what is the understood coefficient?

One Signup and view all the answers

Are constants like terms? (Ex: 2 & 5)

True Signup and view all the answers

What do you distribute if there is no number in front of the parentheses, like in the expression 2 - (x + 3)?

Negative one Signup and view all the answers

What is the goal when solving equations?

Get the variable by itself (isolate the variable) Signup and view all the answers

What are the steps for solving equations?

<ol> <li>Simplify, 2. Move extra terms using + or -, 3. Move the coefficient using Mult. or Division</li> </ol> Signup and view all the answers

What are the steps for solving inequalities?

<ol> <li>Simplify, 2. Move extra terms using + or -, 3. Move the coefficient using Mult. or Division, 4. Flip the inequality, if necessary</li> </ol> Signup and view all the answers

What is the flip rule that is used with inequalities?

If you multiply or divide both sides by a negative number you flip the inequality sign Signup and view all the answers

How do you determine if a graph is a function?

Vertical line test Signup and view all the answers

How do you see if a table, list of points, or mapping diagram is a function?

Check to see if the x repeats and takes you to different y values Signup and view all the answers

What is domain?

Set of all x values Signup and view all the answers

What is range?

Set of all y values Signup and view all the answers

What do you look for on a table if you are looking for intercepts?

Look for the zeros; X-intercept is (#, 0), Y-intercept is (0, #) Signup and view all the answers

What is the zero of a function?

X-intercept, root, or solution Signup and view all the answers

What is the x value of every y intercept?

x = 0 (0,y) Signup and view all the answers

What is the y value of every x intercept?

y = (x,0) Signup and view all the answers

How do you tell if a graph is linear?

It makes a straight line Signup and view all the answers

How do you tell if a table represents a linear function?

Look for a constant rate of change (slope) or plot the points and see if it is a straight line Signup and view all the answers

How do you tell if ordered pairs are a linear function?

<ol> <li>Look for a constant rate of change (slope) or plot the points and see if it is a straight line. 2. Check to make sure it is a function.</li> </ol> Signup and view all the answers

What do we use to find slope if we are given two ordered pairs?

The Slope formula (Delta Y over Delta X) or use a table Signup and view all the answers

What letter represents slope?

m Signup and view all the answers

What is a synonym for constant rate of change?

Slope Signup and view all the answers

What are f(x), g(x), and h(x) the same as?

Y or output Signup and view all the answers

Are f(x) values part of the domain or range?

Range; f(x) = y Signup and view all the answers

If you are asked to evaluate a function given f(3), where do you put the 3?

Plug it in for x Signup and view all the answers

If you are asked to evaluate a function given f(x) = 6, where do you put the 6?

Plug it in for y; f(x)=y Signup and view all the answers

What type of correlation does the situation have: As one variable increases, the other variable decreases?

Negative Signup and view all the answers

What type of correlation does the situation have: As one variable increases, the other variable increases?

Positive Signup and view all the answers

What type of correlation does the situation have: Your grade and the type of hair color you have?

No correlation Signup and view all the answers

What does the y-intercept represent in a real-world problem?

The starting point or one-time event Signup and view all the answers

What does the slope represent in real-world problems?

The value that is occurring MULTIPLE times, Rate of Change (y per x) Signup and view all the answers

If the line on a graph is a horizontal line, what type of slope does it have?

Zero (hint: HOY VUX) Signup and view all the answers

If the line on a graph is a vertical line, what type of slope does it have?

Undefined (hint: HOY VUX) Signup and view all the answers

Given y = 3 - 2x, what is the slope?

m = -2 Signup and view all the answers

Will the axis of symmetry of a parabola be an x=# or a y=# equation?

x=# because it is a vertical line Signup and view all the answers

How do you find the slope of a line from a graph?

Pick two points and count rise over run Signup and view all the answers

Where is the solution to a system of equations on a graph?

The point where the two lines meet/cross/touch Signup and view all the answers

What is the equation for a line with a slope of zero?

y=# (hint: HOY VUX) Signup and view all the answers

What is the equation for a line with an undefined slope?

x=# (hint: HOY VUX) Signup and view all the answers

In a word problem, is the y-intercept the thing that happens one time or multiple times?

One time Signup and view all the answers

Each, per, daily, weekly, monthly, yearly, hourly, and rate are all key words for what?

Slope Signup and view all the answers

What is the equation for the linear parent function?

y = x Signup and view all the answers

What is the equation for the quadratic parent function?

y = x² Signup and view all the answers

How do you solve a system of equations in standard form (ex.ax + by = c)?

Elimination or a Matrix Signup and view all the answers

How do you solve a system of equations in y= format?

By graphing or using substitution to set the two equations equal to each other. Signup and view all the answers

What are the roots of a function?

x-intercepts Signup and view all the answers

Where are the solutions of a quadratic function?

Where the line crosses the x-axis; the x-intercepts Signup and view all the answers

How do you find zeros, roots, x-intercepts, solutions for a quadratic function using a table?

Look for zeros in the y column Signup and view all the answers

How do you find the perimeter of a figure?

Add up all the sides Signup and view all the answers

What is the problem really asking you if it says 'which of the following represents y as a function of x?'

Which one is a function Signup and view all the answers

What inequality symbols are used for dashed lines?

< or > Signup and view all the answers

What does this symbol mean: <

Less than Signup and view all the answers

What does this symbol mean: >

Greater than Signup and view all the answers

How are the equations of parallel lines related?

They have the same slope Signup and view all the answers

How do you tell if a list of points or a table of points are linear, quadratic, or exponential?

Plot them and identify the shapes: linear = line, quadratic = U (parabola), exponential = curve up or down Signup and view all the answers

What do the graphs of quadratic functions look like (what shape)?

U (parabola) Signup and view all the answers

What does changing the m value of a line do?

Changes steepness Signup and view all the answers

What does changing the 4 in y=4x+5 do to the graph?

Changes the steepness Signup and view all the answers

What does changing the y-intercept (b) of a line do to the graph?

Shift/translate up or down Signup and view all the answers

What does changing the 6 in y=7x-6 do to the graph?

Shifts/translates up or down Signup and view all the answers

What does the b in y=mx+b stand for?

Y-intercept Signup and view all the answers

What does the m in y=mx+b stand for?

Slope Signup and view all the answers

How do you write the range of a quadratic with a maximum?

y ≤ the highest point's y value Signup and view all the answers

How do you write the range of a quadratic with a minimum?

y ≥ the lowest point's y value Signup and view all the answers

What point does the axis of symmetry on a quadratic function go through?

Vertex Signup and view all the answers

What does changing the sign of m do to a graph?

Flips direction (reflection) Signup and view all the answers

How do you find the solution to a linear inequality?

Any point in the shaded region or on a solid line (the point will also make the inequality true if it is plugged in for (x,y)) Signup and view all the answers

What do you have to do first before you can type this in to the calculator: x²-6x=10?

Subtract 10 from each side so all terms are on one side of the = Signup and view all the answers

When explaining in words what slope represents, what do you say first, the x quantity or the y quantity?

List what y stands for first ('because you are more important than your eX'); y per x Signup and view all the answers

What does the word 'initial' mean?

Beginning or starting point Signup and view all the answers

What are the four vocabulary words that describe where the parabola crosses/touches the x-axis?

Zeros, Roots, X-intercepts, Solutions Signup and view all the answers

How will the multiple choice answers for slope questions try to trick you?

One of the answer choices will have run/rise or change in x/change in y Signup and view all the answers

Where is a minimum on a parabola?

The vertex (if the parabola opens up); it's the lowest point Signup and view all the answers

Where is the maximum of a parabola?

The vertex (if the parabola opens down); it's the highest point Signup and view all the answers

What do you do first in exponent questions?

Regular numbers, regular rules (e.g., multiply the big numbers in a multiplication problem or divide the big numbers in a division problem) Signup and view all the answers

How do you simplify this: (x+4)(x+2)?

Use the Distributive Property (FOIL) Signup and view all the answers

How do you tell if an equation is linear, quadratic, exponential, or none of these?

Plug it in to y= on the calculator and graph it, make a table and plot points and look at the graph, or read the situation Signup and view all the answers

What changes in the equation to cause a parabola to reflect across the x-axis?

A negative sign in front of the equation (a is negative) Signup and view all the answers

In the vertex form of an equation (y = a(x - h)² + k), what happens to the graph when the h value changes?

Horizontal shift (going the opposite direction of the sign) Signup and view all the answers

From the vertex form (y = a(x - h)² + k), what happens on a graph if you change the 'k' value?

It shifts up or down Signup and view all the answers

What is the domain of most functions/graphs that have arrows on both ends?

All real numbers (written as the infinity statement -∞ to ∞) Signup and view all the answers

Study Notes

Intercepts

X-intercept of y = 2x + 4 is (-2, 0)
Y-intercept of y = 2x + 4 is (0, 4)

Algebra Definitions

Variable: A letter representing an unknown quantity.
Constant: A standalone number in an expression.
Coefficient: The number multiplied by a variable in a term.

Calculator Functions

Change decimal to fraction: Math, 1: Frac, enter, enter.
Use parentheses when substituting values for variables.
Use negative button for the first term or inside parentheses, minus sign for between terms.

Operations

Quotient represents division.
Difference represents subtraction.
Product represents multiplication.

Evaluating Expressions

When evaluating with a long fraction, solve the numerator and denominator separately before dividing.
Exponents entered using the caret key (^).

Simplifying Expressions

Simplification steps include distributing and combining like terms.
Order of operations: Parentheses, Exponents, Multiplication/Division (left to right), Addition/Subtraction (left to right).

Inequalities

Combine like terms using addition.
Flip the inequality sign when multiplying or dividing by a negative number.
Open point for "<" or ">" and closed point for "≤" or "≥".

Functions

A function passes the vertical line test, ensuring x values do not repeat.
Domain: Set of all x values; Range: Set of all y values.

Graphing

Intersection of lines shows solutions to systems of equations.
X-intercept has y value of 0; Y-intercept has x value of 0.
A function represented graphically: Linear functions create straight lines, while quadratic functions form U-shaped curves.

Correlation

Negative correlation: One variable increases as the other decreases.
Positive correlation: Both variables increase together.
No correlation: No relationship exists.

Real-World Applications

Y-intercept indicates starting point in context.
Slope signifies the rate of change, occurring multiple times.
Horizontal lines have a slope of 0; vertical lines have an undefined slope.

Slope & Parabolas

Slope represented by "m".
Roots or x-intercepts are the points where a function crosses the x-axis.
Parabola's vertex indicates maximum or minimum points, which correspond to the axis of symmetry.

Systems of Equations

Solve via substitution or elimination methods.
Systems yield unique solutions where lines intersect.

Manipulating Equations

In the format y = mx + b, "m" represents the slope, "b" the y-intercept.
Shifts up or down occur when changing the "b" value in the equation.

Quadratic Functions

Range of quadratics with maximum values: y ≤ highest point.
Range of quadratics with minimum values: y ≥ lowest point.
To reflect across the x-axis, a negative sign is introduced before the equation.

Summary Techniques

For exponent questions, simplify regular numbers first.
Use the distributive property (FOIL method) for binomials.
For identifying function types, graph inputs to visualize behavior.

General Notes

Understanding constants, variables, and coefficients is crucial for algebraic manipulation.
Keeping track of signs and symbols is vital for accurate calculations and interpretations.
Recognizing the implications of shifts in quadratic functions aids in predicting graph transformations.

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Test your knowledge with these Algebra I reinforced flashcards. This quiz covers key concepts such as intercepts, variables, constants, and coefficients. Perfect for review or reinforcement of foundational algebra skills.