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?
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What are the calculator keystrokes for changing a decimal to a fraction or for reducing a fraction?
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What must you use when substituting in numbers for variables?
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Are negative signs and subtraction signs interchangeable on the calculator?
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What operation is used for 'quotient'?
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What operation is used for 'difference'?
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What operation is used for 'product'?
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What do you do when evaluating an expression that has a long fraction bar?
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How do you enter an exponent in the calculator?
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What is any non-zero number raised to the zero power?
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What are the steps for simplifying expressions?
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What is the order of operations?
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What two things must be the same to combine like terms?
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What operation do we use to combine like terms?
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If there is a variable with no number in front, what is the understood coefficient?
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Are constants like terms? (Ex: 2 & 5)
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What do you distribute if there is no number in front of the parentheses, like in the expression 2 - (x + 3)?
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What is the goal when solving equations?
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What are the steps for solving equations?
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What are the steps for solving inequalities?
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What is the flip rule that is used with inequalities?
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How do you determine if a graph is a function?
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How do you see if a table, list of points, or mapping diagram is a function?
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What is domain?
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What is range?
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What do you look for on a table if you are looking for intercepts?
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What is the zero of a function?
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What is the x value of every y intercept?
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What is the y value of every x intercept?
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How do you tell if a graph is linear?
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How do you tell if a table represents a linear function?
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How do you tell if ordered pairs are a linear function?
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What do we use to find slope if we are given two ordered pairs?
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What letter represents slope?
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What is a synonym for constant rate of change?
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What are f(x), g(x), and h(x) the same as?
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Are f(x) values part of the domain or range?
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If you are asked to evaluate a function given f(3), where do you put the 3?
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If you are asked to evaluate a function given f(x) = 6, where do you put the 6?
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What type of correlation does the situation have: As one variable increases, the other variable decreases?
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What type of correlation does the situation have: As one variable increases, the other variable increases?
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What type of correlation does the situation have: Your grade and the type of hair color you have?
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What does the y-intercept represent in a real-world problem?
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What does the slope represent in real-world problems?
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If the line on a graph is a horizontal line, what type of slope does it have?
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If the line on a graph is a vertical line, what type of slope does it have?
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Given y = 3 - 2x, what is the slope?
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Will the axis of symmetry of a parabola be an x=# or a y=# equation?
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How do you find the slope of a line from a graph?
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Where is the solution to a system of equations on a graph?
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What is the equation for a line with a slope of zero?
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What is the equation for a line with an undefined slope?
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In a word problem, is the y-intercept the thing that happens one time or multiple times?
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Each, per, daily, weekly, monthly, yearly, hourly, and rate are all key words for what?
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What is the equation for the linear parent function?
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What is the equation for the quadratic parent function?
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How do you solve a system of equations in standard form (ex.ax + by = c)?
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How do you solve a system of equations in y= format?
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What are the roots of a function?
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Where are the solutions of a quadratic function?
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How do you find zeros, roots, x-intercepts, solutions for a quadratic function using a table?
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How do you find the perimeter of a figure?
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What is the problem really asking you if it says 'which of the following represents y as a function of x?'
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What inequality symbols are used for dashed lines?
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What does this symbol mean: <
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What does this symbol mean: >
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How are the equations of parallel lines related?
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How do you tell if a list of points or a table of points are linear, quadratic, or exponential?
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What do the graphs of quadratic functions look like (what shape)?
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What does changing the m value of a line do?
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What does changing the 4 in y=4x+5 do to the graph?
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What does changing the y-intercept (b) of a line do to the graph?
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What does changing the 6 in y=7x-6 do to the graph?
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What does the b in y=mx+b stand for?
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What does the m in y=mx+b stand for?
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How do you write the range of a quadratic with a maximum?
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How do you write the range of a quadratic with a minimum?
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What point does the axis of symmetry on a quadratic function go through?
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What does changing the sign of m do to a graph?
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How do you find the solution to a linear inequality?
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What do you have to do first before you can type this in to the calculator: x²-6x=10?
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When explaining in words what slope represents, what do you say first, the x quantity or the y quantity?
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What does the word 'initial' mean?
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What are the four vocabulary words that describe where the parabola crosses/touches the x-axis?
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How will the multiple choice answers for slope questions try to trick you?
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Where is a minimum on a parabola?
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Where is the maximum of a parabola?
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What do you do first in exponent questions?
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How do you simplify this: (x+4)(x+2)?
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How do you tell if an equation is linear, quadratic, exponential, or none of these?
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What changes in the equation to cause a parabola to reflect across the x-axis?
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In the vertex form of an equation (y = a(x - h)² + k), what happens to the graph when the h value changes?
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From the vertex form (y = a(x - h)² + k), what happens on a graph if you change the 'k' value?
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What is the domain of most functions/graphs that have arrows on both ends?
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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.