methods
definitions
solving
representations
practice
100
Make as large as possible.
What is maximize
100
Points where a graph crosses the axes. x-______are points at which the graph crosses the x axis and y-_______are points at which the graph crosses the y axis. On the graph below the x-________is (3, 0) and the y-________ is (0, 6).
What is intercepts
100
Of an equation or inequality is a number or expression that makes the equation or inequality true when substituted for the variable. To find the numerical _____ means to identify all the numbers that make a mathematical equation or inequality true. There may be any number of ______ for an equation or inequality, from 0 to infinitely many. ______-to equations and inequalities in one variable are single numbers. For two variables they are ordered pairs, for three variables ordered triples. Equations with no _________, such as , are never true. Equations with one, several, or many ______, such as are sometimes true, and equations or identities such as are always true.
What is solution
100
A line or curve on a two-dimensional graph that divides the graph into two regions. A _______ line or ______ is used when graphing inequalities with two variables.
What is boundary curve
100
Solve the system using the strategy you have chosen and explain why that choice is best for you. y = 2x −1 y = −(1/3)x + 6
What is (3,5)
200
To _____ an equation or expression is to write an equivalent equation or expression. ________ could involve using the Distributive Property, following the Order of Operations, using properties of 0 or 1, substitution, inverse operations, Properties of Logarithms, or use of trigonometric identities. We usually ______ in order to change expressions or equations into more useful forms or sometimes, just simpler forms.
What is rewrite
200
A point of ________ is a point that the graphs of two or more equations have in common. Graphs may _______ in one, two, several, many or no points. The set of coordinates of a point of _________ are a solution to the equation for each graph.
What is intersection
200
Sometimes in the process of solving equations, multiplying or squaring expressions involving a variable will lead to a numerical result that does not make the original equation true. This false result is called an ______. For example, in the process of solving the equation sqrt(x+3) = 9-x, both sides of the equation are squared to get x + 3 = x^2 − 19x + 81 which has solutions 6 and 13. 6 is a solution of the original equation, but 13 is _______-, because sqrt(13+3) doesn't equal 9-13.
What is extraneous solution
200
A line or curve on a two-dimensional graph that divides the graph into two regions. A ________ or curve is used when graphing inequalities with two variables.
What is boundary line
200
Solve for x: abs(2x+1)=5
What is -3, 2
300
The graph of a _______-_________ _________ is the set of points that represents all solutions to the inequality. A linear inequality divides the coordinate plane into two halves by a boundary line where one half represents the solutions of the inequality.
What is two-variable inequality
300
A ________ that can be written in the form ax + b = c, where a, b, and c are real numbers and a cannot be equal to zero
What are one-variable equations?
300
A _______ is a set of inequalities with the same variables. Solving a _________ means finding one or more regions on the coordinate plane whose points represent solutions to each of the inequalities in the system. There may be zero, one, or several such regions for a ________.
What is system of inequalities
300
The endpoint of a ray or segment on a number line where an inequality is true. For strict inequalities (that is, inequalities involving < or >), the point is not part of the solution. We find _______ by solving the equality associated with our inequality. For example, the solution to the equation 2x + 5 = 11 is x = 3, so the inequality 2x + 5 ≥ 11 has a ___________ at 3. The solution to that inequality is illustrated on the number line at right. A ________ is also sometimes called a “dividing point.”
What is boundary point
300
Solve the system of equations y=2x-2 y=(1/3)x^2+1
What is (3,4)
400
Using inverse operations and reversing the order of operations to solve an equation in one variable or to _____ a function rule in order to write its inverse. For example, in the equation y = x^3 -7, add y and write the cube root.
What is Undoing
400
Graphing ________. When we solve an equation and come up with a solution such as , that means that 4 is the only value that makes that equation true. But when solving inequalities, we get an answer that is also in the form on an inequality .
What are one-variable inequality
400
2(y − 1)^2 + 8 = 80
What is y=-5or7
400
In mathematical optimization, a feasible region, feasible set, search space, or _______ is the set of all possible points (sets of values of the choice variables) of an optimization problem that satisfy the problem's constraints, potentially including inequalities, equalities, and integer constraints.
What is solution region
400
Solve for x: x^2 − 2x − 15 < 0
What is x<-3 and x>5
500
A sequence is an ordered list of numbers and the sum of the terms of a sequence is a series. In an _________, each term is equal to the previous term, plus (or minus) a constant. The constant is called the common difference (d).
What is arithmetic sequence
500
If a, b, and r are real numbers (and if a and b are not both equal to 0) then ax + by = r is called a ________ . (The “two varaibles” are the x and the y.)
What is two-variable equation
500
A ______ is a sequence with the ratio between two consecutive terms constant. This ratio is called the common ratio.
What is geometric sequence
500
A ________ is a set of equations with more than one unknown or variable. The systems we solve most often in this course have two or three equations and two or three variables. ________ are often solved using substitution or elimination to reduce the number of variables.
What is system of equations
500
(5/x)-(10/(x^2+2x))
What is 5/(x+2)
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