Week 9 – precalculus 11

This week in pre-calculus 11 I learned about modeling problems with quadratic function. I was a little bit confused about how to solve that kind of questions but after few practicing, I learned how to solve those questions.

Here is an example:

Week 8 – precalculus 11

This week in precalculus11 I learned about analyzing the quadratic function of the form y=a(x+p)^2+q.  Each of these words represents something on the graph.

a is the coefficient. It shows the stretch or compression of the parabola. If a > 0 parabola becomes skinnier, and if a < 1the parabola becomes wider. Also, a shows whether the parabola opens up or reflect down.

P represents horizontal translation.

q represents vertical translation.

Here is an example:

 

 

Week 7 – precalculus 11

This week in precalculus 11 I learned about discriminant. It was an easy lesson. The expression b^2-4ac, is called discriminant of the quadratic equation because it discriminates among the types of possible solution. Here is an example:

calculate the value of the discriminant of this quadratic equation.

2x^2-8x-4=0

first step: write down the equation first b^2-4ac

second step: write down what is a, b and c

a= 2       b=-8    c= 4

third step: put everything in the equation

(-8)^2-4(2)(-4)

64+32=96

this equation has two real roots so 97> 0

Week 6 – precalculus 11

.This week in precalculus 11 I learned about the quadratic equation. At first, it was a little bit confusing but after memorizing the song for quadratic formula, that was easier for me to solve quadratic equations.

Here is the formula:

Here is an example:

Week 4 – precalculus 11

this week in pre-calculus 11 we learned about multiplying and dividing radicals. at first, I had a little bit of problem with multiplying and dividing radicals but by several practicing, I learned how to solve them; here are the examples:

Week 2 – precalculus 11

This week in Pre calculus11, I learned about the geometric sequence. In this lesson, I had a little bit of struggling when the question gives me two terms and asks for the unknown term. After understanding what the question is asking I learned how to solve this type of questions. Here is an example:

 

 

Week 1 – precalculus 11

This week in Pre calculus11, I learned about the Arithmetic sequence. This lesson was an easy lesson, but I had a little bit of struggling at first when I had to solve the question that seemed a little bit hard for me, but after several practicing, I learned how to solve the question, Here is the Example:

Example 1: How many terms are in the sequence 2, 6, 10, 14,…….,50

first step:

we know the first term is 2, the common difference is 4, and we say the t_n is 50

second step:

the equation is=> t_nt_1 +(n-1)d

third step:

Now we could put  the things that we know in the equation:

50= 2 +(n-1)4

forth step:

we don’t know what is n in (n-1) so we would multiply the common difference which is 4 by n and -1

50= 2 +4n-4

Last step:

so now we put the unknown on one side and the known on the other side

50-2+4= 4n

52= 4n

\frac{52}{4}=\frac{4}{4}

n= 13

so there are 13 terms in that sequence