Show:
Absolute Value Functions
Systems of Equations
Linear Equations and Models
Quadratic Expressions and Equations
Algebra Wizard!!
100
The Absolute Value Function
What is f(x) = |mx+b| + c ANNOTATED SOLUTION f(x) = |mx+b| + c is the correct form of the function that is used to both solve and graph absolute value functions. f(x) is the value of the function or y value. | and | mark the opening and closing of the absolute value brackets. m is the value of the slope. b is used to find the x-value of the vertex when you take -b and divide it by the m value. c is the y-value of the vertex.
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A set of 2 or more equations that use the same variables
What is A system of equations ANNOTATED SOLUTION A set of 2 or more equations that use the same variables is the definition of a system of equations. A system implies that it has more than one of something and they need to have the same variables for us to be able to graph them in the same coordinate plane and be able to solve for the 2 variables.
100
A function whose graph is a straight line
What is a Linear Function ANNOTATED SOLUTION A function can consist of any random assortment of points. Sometimes, these points have direct correlation to each other and when graphed, they form a straight line. There are several equations that represent functions like this including linear equations in standard form, point-slope form, and slope-intercept form. When a function's graph is a straight line, we call this function a linear function.
100
The shape of the graph of a quadratic equation
What is a Parabola ANNOTATED SOLUTION The graph of a linear equation is shaped like a straight line. A quadratic equation is different so its graph will be shaped differently as well. When a quadratic equation is graphed, it looks like a u or an upside down u. This shape is called a parabola.
100
Micah's (Algebra Wizard) favorite unit this semester
What is quadratic equations and formula ANNOTATED SOLUTION I really enjoyed this section both because I found it easy, and also because i really like all of the things that you can do with quadratic equations.
200
The point where the function reaches its minimum or maximum
What is the Vertex ANNOTATED SOLUTION The definition of a vertex is the point where a function reaches its minimum or maximum. By definition, the correct response would be vertex. the vertex is the minimum of a function when its graph opens up, and it is the maximum when its graph opens down.
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Allows you to find exact solutions without using graphs
What is substitution or elimination ANNOTATED SOLUTION There are multiple ways in which you can find the solutions of a system of equations. One way is by using graphing. You graph the system and when you look at the graph, you can see where the 2 lines intersect and that is the solution to the system. Sometimes this method does not work because the exact point of intersection is not clear so you could not find the exact solution to the system. When this occurs, you can find the exact solution through 2 different ways. These are substitution and elimination. They both work and they get the same solution you just use different work to get there.
200
DAILY DOUBLE The point at which the line crosses the y axis DAILY DOUBLE
What is The y-intercept ANNOTATED SOLUTION When 2 lines cross each other they intersect at exactly 1 point. When a line crosses over the y axis, they intersect at exactly 1 point as well. This point is called the y-intercept.
200
Rewriting an expression as the product of its factors
What is Factoring ANNOTATED SOLUTION
200
Micah's least favorite unit
What is factoring equations ANNOTATED SOLUTION i had a lot of problems at first understanding all of the different special types of factoring. This really ruined my overall factoring experience while i understand it well now, i still remember not understanding and being really frustrated.
300
The absolute value of a number
What is a numbers distance from 0 ANNOTATED SOLUTION The absolute value of 3 is 3. The absolute value of -3 is also 3. The definition of the absolute value of a number is its distance from zero ON A NUMBER LINE. When absolute values are used in other circumstances, such as with imaginary numbers, the number is sometimes marked on a graph of a coordinate plane. The absolute value is still the distance from zero, but it is just not on a number line.
300
the way to represent all of the solutions to a system of inequalities
What is shading ANNOTATED SOLUTION The graph of a system of equations involves a coordinate plane with 2 lines on it. With linear inequalities, there is a little bit more to it. You graph the inequality exactly as if it were an equation. Because inequalities are less than or greater than, they involve many solutions rather than just one like an equation. You have to represent all of these possible solutions on the graph of a system of inequalities also. These solutions are represented by shaded sections of the coordinate plane. When you have more than 1 inequality being graphed, you need to find the section of the coordinate plane that is shaded from all of the inequalities being graphed. All of the points in this section are the solution to the system of equations.
300
A set notation used to write solutions to an equation
What is An Ordered Pair ANNOTATED SOLUTION In the coordinate plane, each point has both an x value and a y value. solutions to an equation are points in the coordinate plane so they will have a x value and a y value. An ordered pair is a notation used to write both the x and y values of a point. (x,y) x is the x value of the point and y is the y value of the point.
300
The term of a quadratic equation that distinguishes it from a linear equation
What is the quadratic term ANNOTATED SOLUTION A quadratic equation is different than a linear equation. The quadratic term is the part of the equation that is ax^2. Linear equations do not have this term, so if an equation has this term, it is quadratic.
300
Micah's favorite activity
What is the Teaching Assignment ANNOTATED SOLUTION i think that the teaching assignment really gets the students to learn more about the material they are covering. It takes more understanding to teach a subject and i always find that i have no problems understanding material that i taught years after.
400
y = |x| m=1, b=0, c=0.
What is the parent absolute value function ANNOTATED SOLUTION The parent graph of an absolute value graph or a quadratic graph is the most basic graph from which all other come from. In an absolute value equation, the parent graph is where the vertex is at (0,0) and the slope is equal to 1. This is the most basic graph and the graphs of other equations are varied from this graph by either reflection, stretch, or shrink.
400
A system of equations with no solutions
What is an Inconsistent system ANNOTATED SOLUTION Some systems of equations do not have any solutions. Using the example of a graph, the solution to the system is the point where the lines intersect. There are some lines that run alongside other lines and never intersect with them. These are called parallel lines. If a system of equations involves 2 parallel lines, then the system will have no solution. This type of system is called and inconsistent system.
400
A line that approximates the relationship between the data sets of a scatter plot
What is A Trend Line ANNOTATED SOLUTION A scatter plot is used to graph points of a function that are not part of a linear equation and are not in a straight line. A scatter plot is a coordinate plane that has multiple points plotted but has no line or equation graphed. Sometimes, you need to estimate data from a scatter plot into linear form. When this happens, you would use a trend line. A trend line is a line of a linear equation that averages all of the points in a scatter plot and is the line that best fits the average of all the points.
400
The Product when you square a binomial
What is a perfect square trinomial ANNOTATED SOLUTION One way to write a quadratic equation is in the form of ax^2 + bx + c. This is called a perfect square trinomial. When a perfect square trinomial is factored, it becomes the product of 2 binomials. The process described in this question is doing the same work as factoring except backwards.
400
What Micah needs to work on the most next semester
What is taking notes in class ANNOTATED SOLUTION I usually never take really in depth notes in class because i already understand the material being covered. Usually i do other work in class. This hasn't been a big problem this semester because all of the material was easy and didn't require any notes, but when we get into harder material notes will be a necessity.