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