Algebra I Flashcards Review
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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?

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

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

<p>Math, 1: Frac enter, enter</p> Signup and view all the answers

What must you use when substituting in numbers for variables?

<p>Parentheses</p> Signup and view all the answers

Are negative signs and subtraction signs interchangeable on the calculator?

<p>False</p> Signup and view all the answers

What operation is used for 'quotient'?

<p>Division</p> Signup and view all the answers

What operation is used for 'difference'?

<p>Subtraction</p> Signup and view all the answers

What operation is used for 'product'?

<p>Multiplication</p> 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?

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

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

<p>One</p> 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?

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

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

<p>Variable and exponents</p> Signup and view all the answers

What operation do we use to combine like terms?

<p>Addition</p> Signup and view all the answers

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

<p>One</p> Signup and view all the answers

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

<p>True</p> 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)?

<p>Negative one</p> Signup and view all the answers

What is the goal when solving equations?

<p>Get the variable by itself (isolate the variable)</p> 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?

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

How do you determine if a graph is a function?

<p>Vertical line test</p> Signup and view all the answers

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

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

What is domain?

<p>Set of all x values</p> Signup and view all the answers

What is range?

<p>Set of all y values</p> Signup and view all the answers

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

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

What is the zero of a function?

<p>X-intercept, root, or solution</p> Signup and view all the answers

What is the x value of every y intercept?

<p>x = 0 (0,y)</p> Signup and view all the answers

What is the y value of every x intercept?

<p>y = (x,0)</p> Signup and view all the answers

How do you tell if a graph is linear?

<p>It makes a straight line</p> Signup and view all the answers

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

<p>Look for a constant rate of change (slope) or plot the points and see if it is a straight line</p> 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?

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

What letter represents slope?

<p>m</p> Signup and view all the answers

What is a synonym for constant rate of change?

<p>Slope</p> Signup and view all the answers

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

<p>Y or output</p> Signup and view all the answers

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

<p>Range; f(x) = y</p> Signup and view all the answers

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

<p>Plug it in for x</p> Signup and view all the answers

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

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

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

<p>Negative</p> Signup and view all the answers

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

<p>Positive</p> Signup and view all the answers

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

<p>No correlation</p> Signup and view all the answers

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

<p>The starting point or one-time event</p> Signup and view all the answers

What does the slope represent in real-world problems?

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

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

<p>Zero (hint: HOY VUX)</p> Signup and view all the answers

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

<p>Undefined (hint: HOY VUX)</p> Signup and view all the answers

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

<p>m = -2</p> Signup and view all the answers

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

<p>x=# because it is a vertical line</p> Signup and view all the answers

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

<p>Pick two points and count rise over run</p> Signup and view all the answers

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

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

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

<p>y=# (hint: HOY VUX)</p> Signup and view all the answers

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

<p>x=# (hint: HOY VUX)</p> Signup and view all the answers

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

<p>One time</p> Signup and view all the answers

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

<p>Slope</p> Signup and view all the answers

What is the equation for the linear parent function?

<p>y = x</p> Signup and view all the answers

What is the equation for the quadratic parent function?

<p>y = x²</p> Signup and view all the answers

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

<p>Elimination or a Matrix</p> Signup and view all the answers

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

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

What are the roots of a function?

<p>x-intercepts</p> Signup and view all the answers

Where are the solutions of a quadratic function?

<p>Where the line crosses the x-axis; the x-intercepts</p> Signup and view all the answers

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

<p>Look for zeros in the y column</p> Signup and view all the answers

How do you find the perimeter of a figure?

<p>Add up all the sides</p> 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?'

<p>Which one is a function</p> Signup and view all the answers

What inequality symbols are used for dashed lines?

<p>&lt; or &gt;</p> Signup and view all the answers

What does this symbol mean: <

<p>Less than</p> Signup and view all the answers

What does this symbol mean: >

<p>Greater than</p> Signup and view all the answers

How are the equations of parallel lines related?

<p>They have the same slope</p> 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?

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

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

<p>U (parabola)</p> Signup and view all the answers

What does changing the m value of a line do?

<p>Changes steepness</p> Signup and view all the answers

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

<p>Changes the steepness</p> Signup and view all the answers

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

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

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

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

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

<p>Y-intercept</p> Signup and view all the answers

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

<p>Slope</p> Signup and view all the answers

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

<p>y ≤ the highest point's y value</p> Signup and view all the answers

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

<p>y ≥ the lowest point's y value</p> Signup and view all the answers

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

<p>Vertex</p> Signup and view all the answers

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

<p>Flips direction (reflection)</p> Signup and view all the answers

How do you find the solution to a linear inequality?

<p>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))</p> 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?

<p>Subtract 10 from each side so all terms are on one side of the =</p> 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?

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

What does the word 'initial' mean?

<p>Beginning or starting point</p> Signup and view all the answers

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

<p>Zeros, Roots, X-intercepts, Solutions</p> Signup and view all the answers

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

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

Where is a minimum on a parabola?

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

Where is the maximum of a parabola?

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

What do you do first in exponent questions?

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

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

<p>Use the Distributive Property (FOIL)</p> Signup and view all the answers

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

<p>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</p> Signup and view all the answers

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

<p>A negative sign in front of the equation (a is negative)</p> 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?

<p>Horizontal shift (going the opposite direction of the sign)</p> 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?

<p>It shifts up or down</p> Signup and view all the answers

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

<p>All real numbers (written as the infinity statement -∞ to ∞)</p> 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.

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