One thing I learned this week in Pre Calc 11 is how to write absolute value functions in piecewise notation. We already have learned about absolute values (reference back to week 3 blog post for reminder). This week we learned about piecewise notation, and how to understand and write it for a absolute value function.
Piecewise notation is used to describe a function that has different definitions for different parts of the graph. When writing absolute values we use piecewise notation to describe the absolute value of the number.
In the example below follow the steps I take to write a absolute value function in piecewise notation…
One thing I learned this week in Pre Calc 11 is how to solve systems of equations using substitution. A way to solve a linear system is to use the substitution method. You use the substitution method by substituting one y-value in a equation with the other. While using the substitution method you first substitute y in the second equation with thefirst equation since y = y. After substituting y into the equation and solving for x the value of x can then be used to find y by substituting the number you found, with x. While using the substitution method you can also start by substituting x in the second equation with the first equation.
Below is a example of how I solved a systems of equations using the steps above…
One thing I learned this week in Pre Calc 11 is how to graph linear equations in two variables. A linear equation divides a graph into two sections. A linear equation has variables to the first degree only, and the variables are never squared, cubed, or taken to any other power. A linear inequality looks very similar to a linear equation, the difference between the two is that a linear equation has a “equals” symbol and a linear inequality has a “inequality” symbol. When writing or understanding a graph of a linear inequality we shade one side of two sections divided by the linear equation. The side of the linear equation that is shaded is the region that will “satisfy” the inequality.
To find the region that will satisfy the inequality we choose a point (called the test point) on either side of the slope and plug it into the linear inequality. Then solve the linear inequality. If the inequality sign is true to the numbers then shade in the region, if not shade in the opposite region on the graph.
Below is a example of how I graphed a linear equation in two variables using the steps above…
This week while studying for the midterm I had to look back at couple things from Unit one Arithmetic and Geometric Series and Sequences. To help practice studying for this unit in the mid term, I went through all my notes and picked out the most important things I need to know. I wrote them down on one piece of paper to use while going through and doing questions from this unit.
One thing I learned this week in Pre Calc 11 is how to find the vertex of a quadratic equation that is in factored form. The first step is to find the x-intercepts or “zeros” of the equation. Once you’ve determined the zeros/ x-intercepts, you find the average of the zeros by adding them and dividing them by two. Once you find that, you plug it in as X in the equation in order to find Y. The x and y coordinates are the coordinates to your vertex.
Below is a example of how I found the vertex of a quadratic equation in factored form using the steps above.
One thing that I learned this week in Pre Calc 11 is how to analyze a Quadratic equation in Standard (vertex) form. In the picture below I will explain how to analyze a Quadratic equation in Standard form. This will help me when I need to graph this type of equation.
One thing that I learned this week in Pre Calc 11 is how to solve a chart with the properties of quadratic functions. To chart a quadratic equation you have to know how to tell when the table of value is showing a quadratic equation, instead of a linear equation. A linear equation in a table of value always has a y value (the output) that goes up or down by the same amount each time in the first differences. A quadratic equation in a table of value always has a y value that goes up or down by the same amount each time in the second difference. Below is a example of both a linear equation, and a quadratic equation charted.
When solving for quadratic functions, you should remember that the x intercept is always equal to y=0 and the y intercept is equal to x=0. Keeping this in mind when solving, to find y you simply plug x into the given quadratic function. Below are some examples to visualize how I would solve for y using the table of values and quadratic function.
One thing that I learned this week in Pre Calc 11 is how to solve quadratic equations using the quadratic formula. The quadratic formula is used to solve quadratic equations. It is most often used when a quadratic equation is non-factorable or hard to factor. Below is the quadratic formula..
I insert a, b, and c from ax2 + bx + c into the quadratic formula and solve. Below are some examples of me using the quadratic formula to solve the following quadratic equations…
One thing that I learned this week in Pre Calc 11 is how to solve for a difference if squares. Before solving for a difference of squares you have to know what a difference of squares is.
Looking For a Difference of Squares
To determine if a sequence is a difference of squares there are three main things you should look for. First, you should look if the sequence is a binomial. If the sequence is not a binomial than it can not be a difference of squares. Second, you should look to see if everything in the sequence is a perfect square. Everything in the sequence needs to be a perfect square because when you factor a difference of squares they turn into conjugates of each other. Third, make sure that the binomial is subtraction expression.
Below I will look to see if the expression is a difference of squares using what I learned in the paragraph above. After I determine whether the expression is a difference of squares or not, I will factor.
One thing that I learned this week in Pre Calc 11 is how to solve a question asking to arrange mixed radicals into descending order (greatest to least). I chose to do this as my blog post this week because I forgot how to do this on the Chapter 2 skills check. In order to solve this question first, you have to convert the mixed radicals into entire radicals. This way you can easily tell which radicals are the greatest, and which radicals are the least.
Below is a example of question asking me to arrange mixed radicals into descending order. Follow the example I used to see the steps I took to answer this question, also how I converted each mixed radical into an entire one.