This week in math week 12, we re-learned how to substitute y=mx+b but with a quadratic, to solve the quadratic version, you must have 2 quadratic equations. The first step in this is to make sure Y or X is isolated generally i like to isolate Y,  and make sure they have no coefficients, and that you have an x² to make sure you have a quadratic equation. Now that you have that you have one of the variables isolated, you use that solution and put it into the other solution wherever you see the variable you isolated on the other solution. Next you want to subtract one end to another making one side equal to 0 (Generally you subtract the soltion without x²)          

Now you want to find the 0’s, because this will allow you to find the y axis. Finding the 0’s will help you complete the equation. Once you find the 2 zero’s, you replace it in any of the equations finding the y axis but it has to be the same equation.

This week in math, we learned how to graph inequalities and systems of equations. This week, we combined our last 2 units and made it into one (Solving Quadratics, and Graphing inequalities and systems). We learned that if the equal sign has a line on the bottom which means equal that it will have a solid line when graphing. $slatex y\le4x+5$. Knowing this we can add a point to check which part to shade in, in this case i used (-2,1)

-2>4(1)+5 =      -2> 8+5

This shows us that we need to shade the bottom side of the graph, because the test points for this solution was not true.

This week in math, I learned how to find the X intercepts in the standard form. I learned this late, but i still learned it in week 9. So to find the X intercepts we have to go back to our last chapter Solving for quadradics. First you would isolate to make X by itself so i subtracted by 1, then after that i sqaure rooted everything to get rid of the brackets, the from there i added 2 to the other side make it 2+/- square root of 1.

This week in math, we learned how to use the X intercepts to find the Line of symmetry. To find the LOS, you take both X intercepts and you add them together then divide by 2. So in the picture below, the X intercepts are -4,0 and 2,0. 2-4/2= -1. Thats the line of symmetry.

This week in Pre calc 11, I learned how to graph the vertex. I learned that when you are given the standard form, you can graph the vertex. In the brackets, you have the X value but a cool thing is that whatever number is in there, you change the sybol. So if it is -3 it really means +3. and the number right outside the brackets is the Y value; so given y=a(x-3)+3, we can tell that we need to graph (3,3) and that is our vertex.