Algebra 1 Review and Vocabulary

relation : set of ordered pairs

ordered pair : the x and y coordinates of a point on the coordinate plane (x,y)

domain : set of all of the possible x-values. INPUTS

range : set of all the possible y-values. OUTPUTS

other names for "y" : range, dependent variable, output

vertical line test : a relation is a function and passes the vertical line test if when a vertical line is drawn through the graph, it touches the graph only ONE time.

graph of a quadratic function :

Quadratic Parent Function :

graph of exponential growth function :

Graph a parabola using a table :

changing the "m" in the slope-intercept form of the equation of a line changes what? : the steepness of the line

changing the "b" in the slope-intercept form of the equation of a line changes what? : moves the line up or down the y-axis.

what slope does a VERTICAL line have? : undefined slope

what is the x-intercept? : the point where the graph crosses the x-axis. It has the coordinates (x, 0)

How do the slopes of parallel lines compare? : They are the same

How do the slopes of perdendicular lines compare? : They are opposite and fraction is flipped. Example: lines with the slopes -2 and 1/2 are perpendicular.

What is a quadratic equation or function? : an equation of function that has "x-squared" as its highest order exponent.

Where are the solutions of a quadratic function? : at the x-intercepts. They are also known as zeros and roots.

What is the "rate of change" on a graph? : Slope

Mean (Average) : Add up all the data points, then divide by however many data points there were. Ex. 3,6,93+6+9= 18 /3 = 6

Whole numbers : Start with 0, 1, 2, ......

Natural numbers : Counting numbers: 1, 2, 3, ......

Quadratic Formula : In standard form, ax^2 + bx + c, where a, b, and c (Just the numbers) can be plugged into the quadratic formula to find the x-intercepts, roots, zeros, or solutions.

Completing The Square : Isolate x^2 + bx on one side, move the number to the other side of the equal sign. Take b, divide by 2, then square the result. Add that number to both side. It will then factor into a perfect square.

When do you flip an inequality symbol? : Anytime you multiply or divide by a negative number.

Explain each step in solving an equation. : You may have to list the steps you performed explaining what you did, step by step. Know how to justify your solutions.

How to use the Discriminant when solving the Quadratic Formula? : If the discriminant is positive, you will have 2 solutions or x-intercepts. If the discriminant is zero, you will have 1 solution or x-intercept. If the discriminant is negative, you will have No Solution (or really a complex solution (imaginary) in the form (a + bi)

Factoring with 4 terms : Solve by grouping. Group two sets and then factor those two groups.

The solution to a system of linear inequalities : The intersection of the two half-planes.

Interpret parts of an expression : Examples such as: C= 250 + 35m, Where C is the cost for renting a car. They pay $250 plus $35 for every extra mile they drive. You have to interpret what the numbers and variables mean in the form of a word problem.

Sales Tax : Is added on to the cost of the item. To find the amount to add, multiply the cost of the item by the percent of tax.

y= and f(x)= : These are the same. They can be interchanged with one another. f(x) simply lets you know the equation is a function. Can also be written with other variables like g(x), p(x), etc.

Axis of Symmetry : The equations x=0 is the axis of symmetry for a parabola in standard form.

End Behavior : Describes what is happening to the graph overall as the x-values change. As the x-values decrease, does the graph seem to go up or down? As the x-vales increase, does the graph seem to increase or decrease? This represents the end behavior as being positive or negative.

Step-Function Graph : A function that is not continuous. It has levels which represent the y-value for a set of x-values.

Distinguish between situations that can be modeled with linear functions and with exponential functions. : A linear function would be best for situation in which something is increasing at a constant rate. An exponential function is best for situations in which the rate increase over time. EX. The growth of bacteria cells in a petri dish would be exponential growth.

Geometric Sequence : A pattern in which you multiply or divide each term by the same number.

Which quantity increases fastest? : exponential functions > quadratic functions > linear functions

Correlation : Positive Correlation, Negative Correlation, or No Correlation.

Correlation Coefficient : A number between -1 and 1 that tells you if you have a strong or weak correlation. It also lets you know if it is a positive or negative correlation.

Interquartile Range : Q3 - Q1

Normal Bell Curve : Let's you know where you should find most of your data.

Joint and Marginal Frequencies : Joint is the individual data in the middle. Marginal is the sum of the data for each row or column.

Conditional Relative Frequencies : Comparing the individual data to the whole, represented as a percentage.

Sum : Add

Difference : Subtract

25% of what is 150? : 0.25 * x = 150. To solve you divide by 0.25.

Seven "less than" a number : n - 7 You subtract 7 from the number.

Mixed Number to Improper Fractions : Multiply, then add! Keep the same denominator.

Improper Fractions to Mixed Numbers : How many times will the denominator go into the numerator without going over. Then how many little pieces are left over.

Exponent Rules : There are a bunch!

Perfect Squares : 1, 4, 9, 16, 25, 36, 49, 64, 81, 100, 121, 144, 169, etc. The resulting number when you multiply a number times itself. EX: 4 X 4 = 16

Standard Form of a line : Ax + By = C NO fractions, NO decimals, A has to be positive!

Direct Variation : Set up a proportion and solve. y1/x1 = y2/x2