In week 13 we continued to learn about chapter 8. we did lessons 8.2, 8.3, and 8.5.
In lesson 8.2 we learned about absolute value equations.
In lesson 8.3 we learned graphing reciprocals of linear functions.
In lesson 8.5 we learned graphing reciprocals of quadratics.
It is really fascinating to see how the reciprocals look in a graph because they all look very different from each other. there were also different numbers of parent functions the a parabola has affects the shape of the hyperbola. 0 root, 1 root and 2 roots all have different graph shape.
It was also cool to learn the in the hyperbola will never cross along the X axis.
In week 12 we learned lesson 5.5 and reviewed for our test.
One thing that I learned is how to put a quadratic equation and linear equation and put them together to find the root (x) and replace in the original equation to find (y)
Example
y = 3x + 7 and
y = X2 + 4x +3
X2+4x +3 = 3x +7
Then you move it all to either side but you should try to keep the X squared (X2) positive.
For week 11 of pre calc 11 we continued learning about unit 5, graphing systems and inequalities, lesson 5.2, 5.3, 5.4.
I learned about having different lines on your graph due to the different symbols that are in your equation. If the symbol is < then the line is the graph is dotted. If the symbol is ≥ then the line in the graph is solid.
we also learned about solving systems graphical and we learned how many solutions each system could have. parabolas can have 0,1,2, or infinite.
4.5 and 4.6 focused on the 3 formulas: General, Standard and Factored Form. in the lessons it taught us how to convert one form to another to find out different parts to the parabola.
Week 8 we began reviewing for the mid term and started lesson 4.
In lesson 4.1 we learned about new concepts like the vertex. A vertex is the highest or lowest point on the parabola graph. Other vocabulary we learned were:
Vertex: Lowest/highest possible point
Congruent graphs: if the graph has the same shape as the parent function (y = X2)
The x-intercepts: the point were the line passes through the x-axis
The y-intercepts: the point were the line passes through the y-axis
Direction of opening: Whether the graph opens down or up ( minimum-up) (Maximum-down)
Axis of symmetry: the point that splits the graph down vertically
We also used the table of values for looking at outputs of Y values.
For week 7 we had the final lesson in unit 3 and then had a unit test.
In the lesson we learned a new simple concept or equation b^2-4ac
This formula determines if the equation is even solvable or not and ow many roots it will have.
We can then completely solve the formula if the product is bigger than 0. If the product id bigger then 0 it will have either 2-1 roots and if it is equal to 0 it will have 1 root.
In 3.2 we learned that firstly, linear equations only ever have 1 solution, but if the equation is quadratic, meaning it was a degree of 2, there could be 2 solutions.
Using the formula: Ax^2+ Bx+ C=0 techniques like the zero product law and in polynomials we also use isolating variables to find the values of x.
In lesson 3.3 we learned concepts for perfect square trinomial like you can chop B in half and square it to find C.
This week we learned about adding and subtracting radical expressions. There are some tings you need to remember when adding and subtracting radicals. Before you start doing any adding or subtracting you must remember to put all radicals into there simplest form you can. It makes it easier when you start doing the equation. Another thing to remember is that only the radicals with the same radicand can be combined together. One more thing you should remember is that when adding and subtracting the radicand will not change but the coefficient can change but it depends on the equation .
At the beginning it was sort of easy to figure out but as we continued on it was become much more difficult by the minute. I have found some strategies to help me. The tic tac toe formula that we were shown helps a lot. Where the answer is the same no matter if it is diagonal horizontal or vertical.
