This week we learned the vertex form and how to use clues to figure out to graph it.

y = a(x – p)² + q

Each letter signifies a part on the graph,

A= The thickness of the parabola

P= the horizontal slide

Q= The vertical slide

If A is smaller then 1 then the parabola will be thicker, but the bigger the number the thiner it is. Keep in mind for P that if the number is positive inside the brackets it will be negative on the graph because it is a double negative.

Lets say that out equation is  y = (x – 2)² + 3:

Step one: We want to find the vertex which would be (2,3)

Step two: Figure out A and how we should graph it

Step 3: Since A=1 in this equation it will be up 1 over 1 then up 3 over 1, up 5 over 1 etc.

This will be your default pattern when A=1, if it is any other number you will adjust it by either dividing that pattern or multiplying by that pattern. ex// A= 3

Pattern would be 3,9,15 etc

*COMPUTER WOULD NOT LET ME INSERT PHOTOS*

will fix issue by next week

What I learned in PreCalc 11 this week was what a discriminant is. The discriminant is a part of the quadratic formula (red in picture below) and it tells us if there is 2, 1, or 0 solutions.

The red is the formula used to find the discriminant.

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How we know is that if the final result of  is > 0, then it has 2 solutions. If the answer is = 0, then it has 1 solution and if the answer is < 0 then it has no solution.

This Week we worked on 3 different ways on working with trinominal and how to factor them, they are:

Factoring

Completing the Square

Quadratic Formula

Im not going to go through factoring because I explained it in last weeks blog post.

completing the square-

probably the most complicated way to factor in my option because in order to do this process you need to move the third term and bracket the first 2. Then half the square the second term, the one inside the bracket will be positive and then one outside the bracket will be negative. Keep in mind if the first term has a coeficial you have to times the number by the coeficiant outside the bracket. To made this more clear I will show you a photo below.

Quadratic formula-

This one is quite simple,e and will work almost all the time. A= the first term B= The second term and C= the third term. All you have to do now is plug it in the quadratic formula and do the math. Like shown below.

This week we learned about:

-Absolute Values

– Roots

– Radicals

Absolute values

We learned this week what absolute values are and how to properly go about them. Anything inside the absolute value “bracket” will always end up being positive. For example: |12 – 15 | = +3

Make sure you always do all the calculations before you turn the answer positive.

Roots and Radicals: 

We learned the terms this week. The number in front the square root sign is the coefficient, the small number connected to the square root is the index and the number inside is called the radicand. We learned that the index is a very important clue for the equations because it tells us is the number in the radicand spot can me both negative and positive or only positive. Even number index can only be positive while uneven index can be either. Also simplifying equations, the index is important because it tells us what we can take out to become the coefficient. if the index is 2 we take groups of two.