Properties of Real Numbers
Linear Equations
Solving Systems Algebraically
Modeling Data with Quadratic Functions
Personal Math Growth
100
For addition, this property is a+b is a real number and for multiplication, the preoperty is ab is a real number
What is the closure property? I chose the closure property because it was an important concept for the section. The closure property is important for the more complicated math in advanced algebra.
100
A function whose graph is a line
What is a linear function? I chose this because it was significant to the learning. Linear functions appear throught the chapters we have covered this semester and will cover next semester.
100
systems that have the same solution
What is the definition of equivalent systems? I chose this because it was an important piece to know for future reference for the other chapters. You found a lot of probelms in the homework and tests that had same solutions.
100
a function that can be written in the standard form f(x) = ax^2 + bx + c
What is a quadratic function? I chose this because it was important for the section and chapter which dealt mostly with quadratic functions. This section covered the basics of the quadratic function.
100
retakes
What is something that Jacob did afterschool to recieve a better grade on tests?
200
its distance from zero on the number line
What is the definition of the absolute value of a real number? I chose the definition of the absolute value because it is important for the rest of math in advanced algebra. It is seen throughout the book and a lot of the absolute value was in gaphs.
200
the point at which the line crosses the y-axis
What is the y-intercept? I chose this because it was needed to understand the graphing involved with this section. Other chapters also covered graphing so you needed to know the y-intercept.
200
Elimination gives an equation that is always false. The two equations in the system represent parallel line. The system has no solution.
What is { 2x - 3y = 18 {-2x + 3y = -6 I chose this because it went over what to do if there aren't any solutions to the equation. You would solve it like this: {2x - 3y = 18 {-2x + 3y = -6 ------------------ 0 = 12 Elimination gives an equation that is always false. The two equations in the system represent parallel lines. The system has no solution. This would be the final answer for the homework or tests.
200
the graph of a quadratic function
What is a parabola? I chose this because it was verhy important to the learning of the section and the rest of the chapters. The chapter deals with parabolas so it was very important to understand this.
200
homework
What is something that Jacob should complete on time for next semester?
300
-5/16
What is the opposite reciprocal of -3.2? I chose the opposite reciprocal because it was important to the lesson and you learn about it more than once. What you do is do the opposite of -3.2 which is 3.2. Then you do the reciprocal of 3.2 which is 1/-3.2 = 10/-32 =-5/16.
300
Ax+ By = C
What is the standard form of a linear equation? I chose this because it was important to understand for further learning in the next chapters. Linear equations were the basics of graphing which was needed for other chapters.
300
(-2, 3)
What is {3x + 7y = 15 {5x + 2y = -4 I chose this problem because it also was very important to the section. This shows how to solve an equivalent system. This is what you would do: {3x + 7y = 15 (multiply this by 2) {5x + 2y = -4 ( multiply this by -7) 6x + 14y = 30 -35x -14y = 28 ------------------ -29x = 58 Add X = -2 Solve for x 3x + 7y = 15 Choose an original equation 3(-2) + 7y = 15 substitute the value of x -6 + 7y = 15 Simplify 7y = 21 y = 3 Solve for y The solution is (-2, 3) This is the answer and work you would need to provide for the quizes, homework, and tests.
300
the line that divides a parabola into two parts that are mirror images.
What is axis of symmetry? I chose this because it was very important to the learning and the section. With graphs for this section and chapter, you would have to label the axis of symmetry and know how to solve for it.
300
studying for tests
What is something that Jacob should do to succeed in math next semester?
400
all the numbers that can be written as quotients of intergers, each qoutient must have a nonzero denominator, some rational numbers can be written as terminating decimals, all other rational numbers that can be written as repeating decimals.
What is rational numbers? I chose this problem because rational numbers were important to the section. Rational numbers showed up more in other sections of the semester with some of the answers that were given.
400
y = mx + b
What is the slope-intercept form? I chose this because to graph you need to know this form and that was very important to the lesson. The slope-intercept appeared in other chapters so it was important to understand it.
400
Elimination gives an equation that is always true. The two equations in the system represent the same line. the system has an infinite number of solutions: {(x,y) | y - 2x - 3}
What is { 2x - y = 3 {-2x + y = -3 I chose this because it is very important to the lesson and section. You need this information for the rest of the chapters that cover graphing so it was a major concept. This problem shows what to do if the problem has an infinite number of solutions. This is what you would do: { 2x - y = 3 {-2x + y = -3 ------------------ 0 = 0 Elimination gives an equation that is always true. The two equations in the system represent the same line. The system has an infinite number of solutions: {(x,y) | y = 2x -3}. This is the answer you would need to provide on quizes and tests.
400
the point at which the parabola intersects the axis of symmetry
What is the vertex of a parabola? I chose this because it was very important to the section and chapter. On graphs, you would have to label the vertex and know how to solve for the vertex.
400
warm-ups and exit tickets
What is something that Jacob used to review and better understand the lessons?
500
(a+b) +c = a+(b+c)
What is the associative property? I chose another property because the properties were importing throught this semester and the other chapters. The associative property was important in solving some of the equations.
500
because the value of y depends on the value of x, y is called ________ and x is called ________
What is dependent variable and independent variable? I chose this because you needed to know this information for describing a graph in further lessons as well as this section. Dependent variable and independent variable is needed for knowing if the x or y is domain or range.
500
(2.5, -2)
What is the solutions of {4x +3y = 4 {2x - y = 7 I chose this because this is showing how you would solve a problem by substitution which was very important for this section. This is what you would do: {4x + 3y = 4 {2x - y = 7 2x - y = 7 y = 2x - 7 4x + 3y = 4 4x + 3(2x - 7) = 4 Substitute for y 4x + 6x - 21 = 4 Distributive Property 4x + 6x = 25 x = 2.5 y = 2x - 7 y = 2(2.5) - 7 Substitute for x y = -2 The solution is (2.5, -2) This is how you would solve this problem. Other sections and chapters looked over this problem.
500
this is a quadratic function, quadratic term: 2x^2, linear term: -5x, and constant term: -12.
What is y = (2x + 3) (x - 4)? I chose this because it shows how to determine if a function is quadratic or linear. This is what you would do: y = (2x = 3) (x - 4) = 2x^2 - 8x + 3x - 12 Multiply = 2x^2 - 5x - 12 Write in standard form This is a quadratic function. Quadratic term: 2x^2 Linear term: -5x Constant term: -12 This is how you would solve for the problem.
500
portfolio
What is something that Jacob enjoyed working on and thought it was very creative?
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