Mistake of the week-11

Math Vocabulary:

Coefficient– Number that represents a constant value, usually multiplies the expression.

Factorize/ factor/ factoring– In math factoring or to factor is to find the smallest numbers that multiplied together will give you the original number. This is used so you can work with simpler and smaller numbers.

Ex: 250= 25 x 10, you can still make those numbers smaller, 25= 5 x 5 and 10 = 2 x 5.

Therefore it will end up being 250 = 5 x 5 x 2 x 5.

Quadratic Function– A function in which the equation’s highest exponent is 2.

Parent Function– The parent function for quadratic equations is y=x^2. A parent function is the simplest function that follows a certain set of rules.

Ex: “Quadratic functions have a variable with a maximum exponent of 2”

The simplest function that still follows this rule is y= x^2.

Vertical Translation– When the parent function is changed, the graph will move from its original position. If the graph was moved up or down, it means that it translated vertically.

Horizontal Translation– If the parent function is changed and the grah moved to the right or to the left from its original position, then it means it translated horizontally.

Stretch– This is a coefficient at the beginning of the equation. It determines how wider or narrow the graph will be compared to the parent function. The parent function has an invisible coefficient of 1.

Reflection– When the graph is going down instead of up, it is called a reflection in the x-axis.

Axis– A line used as reference point, in a graph the line that goes from top to bottom is the “y-axis,” and the one across is the “x-axis.”

Coordinates– A set of values that show an exact position, a point in a graph.

Parabola– It is the proper name for the graph of a quadratic equation.

Vertex– The most important part of a graph, is where your graph starts.

Inequalities– A statement that identifies if two things are equal to each other, greater, or smaller than the other. Symbols used: less than <, greater than >, less or equal than ≤, less or equal than ≥, not equal to ≠ and equal to =.

Best mistake of the week:

Workbook Page 437, number 1c:

My mistake:

Inequalities are easy, however, when we need to solve them from a graph it was more confusing than I thought it would be. Finding the x-intercepts was really easy but when it was time to write the solutions for greater and less than zero, it was more challenging.

Why is this important? 

If the symbols in an inequality are not written properly, the answer will not make sense. For example, if the solution you write is x>-2 and x>2; the answer will not be correct because it would show a number-line like this one:

It would mean that even if you say x=1, it would only be true for one of the values for x. This is the main reason of why my initial answer was wrong, you should not have both variables have the same inequality symbol (= might be one of the exceptions but only when they are asking for the solution to be =0).

What I did:

I could not understand how to analyze the graph to get the right answer.

For c), I got the answer x<-5 and x<7.

My error was mostly a sign error, something larger than -5 would be -4, -3, -2, -1, 0, etc. Therefore, it would be to the right of the number line. However, I thought it was to the left because I did not understand the graph fully.

Solution:

After I analyzed the graph, the answer was clearer. I was able to understand how the symbols were supposed to be written and which side of the graph I had to focus on.

It will be easier to understand graphs from now on.

The solution is correct.

Mistake of the week-10

Math Vocabulary:

Coefficient– Number that represents a constant value, usually multiplies the expression.

Factorize/ factor/ factoring– In math factoring or to factor is to find the smallest numbers that multiplied together will give you the original number. This is used so you can work with simpler and smaller numbers.

Ex: 250= 25 x 10, you can still make those numbers smaller, 25= 5 x 5 and 10 = 2 x 5.

Therefore it will end up being 250 = 5 x 5 x 2 x 5.

Quadratic Function– A function in which the equation’s highest exponent is 2.

Parent Function– The parent function for quadratic equations is y=x^2. A parent function is the simplest function that follows a certain set of rules.

Ex: “Quadratic functions have a variable with a maximum exponent of 2”

The simplest function that still follows this rule is y= x^2.

Vertical Translation– When the parent function is changed, the graph will move from its original position. If the graph was moved up or down, it means that it translated vertically.

Horizontal Translation– If the parent function is changed and the grah moved to the right or to the left from its original position, then it means it translated horizontally.

Stretch– This is a coefficient at the beginning of the equation. It determines how wider or narrow the graph will be compared to the parent function. The parent function has an invisible coefficient of 1.

Reflection– When the graph is going down instead of up, it is called a reflection in the x-axis.

Axis– A line used as reference point, in a graph the line that goes from top to bottom is the “y-axis,” and the one across is the “x-axis.”

Coordinates– A set of values that show an exact position, a point in a graph.

Parabola– It is the proper name for the graph of a quadratic equation.

Vertex– The most important part of a graph, is where your graph starts.

Best mistake of the week:

Chapter 4, Skills Check #1, number 5:

My mistake:

I can write the equation of the parabolas, however, when it comes to identify the stretch it was confusing. When I see that the parabola reflects on the x-axis (goes down), I know it has a negative stretch, but I did not understand how we were supposed to see the pattern when it was getting narrower or wider.

Thankfully, my tablemates helped me figure it out and now is really easy.

Why is this important? 

If you do not know how to identify some part of the graph, the equation you get will probably be incomplete too.

What I did:

I asked one of my tablemates, to help me figure out how to identify the stretch. Turns out it was really easy, and you only need to look how far up or down you will meet the line if you look at the block next to the vertex.

Ex.

This is the parent function: y=x^2

The vertex is at (0,0), and the stretch is 1.

*Every two blocks, I count it as 1 block*

This is a function that has a stretch, vertical translation and horizontal translation.

The stretch of this function is 2, and it has a vertical translation of 2, and a horizontal translation of -4.

The equation then is: y= 2 (x-4)^2 + 2

I know it has a stretch of 2 because if I go one block besides the vertex:

Vertex (4,2)

I will go to point (5,2) or (3,2), and count how many blocks away I will hit the line.

It hits the line after 2 blocks, at (5,4) or (3,4).

Solution for the skill check problems:

These answers are right now, and I now know how easy it is to search for the stretch in graphs.

Mistake of the week-9

Math Vocabulary:

Coefficient– Number that represents a constant value, usually multiplies the expression.

Factorize/ factor/ factoring– In math factoring or to factor is to find the smallest numbers that multiplied together will give you the original number. This is used so you can work with simpler and smaller numbers.

Ex: 250= 25 x 10, you can still make those numbers smaller, 25= 5 x 5 and 10 = 2 x 5.

Therefore it will end up being 250 = 5 x 5 x 2 x 5.

Like terms– Terms that have the same base and same exponent. Ex: x and x^2 are not like terms because they do not share the same exponent. xy^3 and 4xy^3 are like terms because their variables and exponents are the same (the coefficient is the only thing that can different in like terms)

Binomial– An algebraic expression consisting of two terms. Ex: 24x – 8

Polynomial–  An algebraic expression consisting of more that two terms. Ex:

Conjugate– Every binomial has a conjugate. This conjugate is the same binomial but you change the middle symbol. Ex: The conjugate of 2x + 8 is 2x – 8. As you can see you change the symbol between both terms.

Zero pairs– A set of two numbers that when added together equal zero.

Quadratic Equation– An equation in which the highest exponent of a function is 2. The equation has two solutions.

Best mistake of the week:

Chapter 5, page 312, #6b:

Solve the equation 4x^2 – 11x – 3 = 0, by using the quadratic formula.

My mistake:

When using the quadratic formula you have to pay attention to the symbols before the numbers (whether the number is negative or positive), I mistakenly wrote down the negative numbers as positive.

Why is this important? 

If you do not write down the things correctly it will change the solution, and it could even make it an impossible/prime equation.

What I did:

Using the quadratic formula is really easy, the only thing you need to do is to pay attention to the details of your equation.

Solution:

The solution is pretty straightforward because is a attention issue rather than a ability to solve math problems issue.

An easy way to avoid this it to put your numbers in brackets, this will help you focus better, and you will be able to write the right numbers and not get anything wrong.

Another example:

Mistake of the week-8

Math Vocabulary:

Coefficient– Number that represents a constant value, usually multiplies the expression.

Factorize/ factor/ factoring– In math factoring or to factor is to find the smallest numbers that multiplied together will give you the original number. This is used so you can work with simpler and smaller numbers.

Ex: 250= 25 x 10, you can still make those numbers smaller, 25= 5 x 5 and 10 = 2 x 5.

Therefore it will end up being 250 = 5 x 5 x 2 x 5.

Like terms– Terms that have the same base and same exponent. Ex: x and x^2 are not like terms because they do not share the same exponent. xy^3 and 4xy^3 are like terms because their variables and exponents are the same (the coefficient is the only thing that can different in like terms)

Binomial– An algebraic expression consisting of two terms. Ex: 24x – 8

Polynomial–  An algebraic expression consisting of more that two terms. Ex:

Conjugate– Every binomial has a conjugate. This conjugate is the same binomial but you change the middle symbol. Ex: The conjugate of 2x + 8 is 2x – 8. As you can see you change the symbol between both terms.

Zero pairs– A set of two numbers that when added together equal zero.

Quadratic Equation– An equation in which the highest exponent of a function is 2. The equation has two solutions.

Best mistake of the week:

Chapter 3, Factoring with fraction and decimal coefficients:

My mistake:

Last week we learned the completing the square method. This is more difficult is you are doing it with fractions, I’ve tried some in the workbook and I think I can understand them now. I wanted to write a blog about it to refresh my memory and get better at it.

Why is this important? 

These different methods to factor will help you be more efficient.

What I did:

Rule #1: In a trinomial the x^2 has to have a coefficient of 1. To do this divide all the expression by the leading coefficient in x^2 (only if there is one.) It is also recomendable for it to be positive so if it is not try to divide by the negative coefficient.

Like before, for these problems you have to focus on the first two digits in the trinomial (x^2 and #x), put them into a square and compare the value on the low right side in the square and the last digit of the trinomial. Remember: If the value you get is bigger than the one you need then the symbol you writer down is negative, in the contrary it will be positive.

See example for a visual explanation.

Solution:

Another example:

I hope this helped 🙂