This week I learned how to find different angles in standard position. First if they give you the point, then you have to determine the side lengths of the triangle. Then you use pythagoreas theorm to determine the hypotenuse. After that, then you use SOH CAH TOA to find the angle.
This week I learned how to add and subtract rational expressions.
First is to check the denominator, if they’re the same then you can go ahead and add or subtract straight across, if not then you will have to bring the denominator up and distribute it. After that it’s just combining like terms.
This week I learned how to multiply rational expressions. First you have to see if you can factor anything, next step is to start cancelling out common factors, once they’re cancelled out, then you can either leave it or divide if needed.
This week I learned how to solve absolute value equations. This question asked to use algebra to solve so I have to find the roots of the equation. Usually you would need to do one positive equation and one negative, but for this case the positive gave me both roots. All I had to do was move the 2 over to the other side of the equation, then factor it out. That gave me both of my roots. The negative one didn’t work for this equation as well.
This week I went back and looked at solving quadratics. First step is to look at the “a value” if it’s just x2
then it’s a lot easier to work with. Next step is to find the factors of the “c value” and so it and the “a value” can add to the “b value.” last step is to make it a zero pair by putting the opposite sign to cancel it out.
This week I learned how to solve systems of equations algebraically. First step is to isolate the variable, in this case I didn’t have to isolate, next is to substitute the x and y into the other equation, and the last step is to solve.
This week I learned how to determine weather a point is going to be a solution in a inequality.
First you have to move either x or y over, in this case the y was easier to move because it was originally negative. After you move your x or y over, then you plug in the point that you have to find out if it’s a solution or not. If you plug everything in and solve, it’ll be a solution if the inequality is true.
This week I learned how to use standard form, from standard form you can find the vertex, and to find the y intercept, you just plug in 0 where x is and solve for the rest of it. If you find where the parabola opens and where the vertex is, you can tell how many x intercepts there will be, in this question the parabola opens up and the vertex has both positive numbers so there were no x intercepts.
This week I learned how to find the discriminant. To find the discriminant, you take the b2 – 4ac
from the original quadratic formula, the discriminant is how you can find out how many roots the quadratic equation is going to have. If the discriminant above 0 it will have 2 roots, if the discriminant is 0, you will have 1 root, and if the discriminant is negative, there are no roots.
This week I learned how to use the table of values in a quadratic function to find the vertex and x intercepts. You can find the vertex on the table of values by plugging x into the function and then on the table of values you look for either the highest or the lowest point on the y.
