II learned this week in Pre Calc 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…
I This week in Pre- Cal 11, I learned this week 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! 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. never choice a point in the graph .
Below is a example of how I graphed a linear equation in two variables using the steps above…
This week in Pre- Calc, we were studying for the math midterm. I decide to look back at the very first unit, since that would re-jog my memory. Week 1 : Arithmetic and Geometric Series and Sequences. I believe the most beneficial way to help me prepare for the mid to was to look back and wright out the key things on one piece of paper.
I learned in Pre Calc this week how to find the vertex of a quadratic equation that is in factored form. Here is how you find it: 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.
During this week of Pre-cal i learned 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.
During Pre-Cal this week i learned 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 (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.
This week in pre – cal, we got taugh 3 ways of doing an quadratic equation. 1. Factoring 2. Square rooting 3. Quadratic formula. I will show all 3 ways of solving an quadratic equation. HINT : always trying to isolate the variable