Question

Please help me with this assignment! It's on Quadratics. I will post the questions in a second, and give a medal to the one who helps the most!

Answer 1

1.Your friend runs up to you, scared that he is not ready for the upcoming quadratics test. To help him study, you will create four different quadratic functions. Then demonstrate to him how to rewrite each function as a group of factors, if possible. •The function f(x) is a difference of squares.
•The function g(x) is a sum of squares.
•The function h(x) is a perfect square trinomial.
•The function j(x) can only have a GCF factored out of it.



2.Given the function k(x) = x2, compare and contrast how the application of a constant, c, affects the graph. The application of the constant must be discussed in the following manners: •k(x + c)
•k(x) + c
•k(cx)
•c • k(x)




3.Explain the grouping method of factoring. Describe a scenario when the grouping method would be preferred over other methods and provide an example of this type of problem.

4.Graph one of your 2nd degree functions from question 1. Identify which function you used and the key features of your graph. Explain how to find them algebraically.

5.Using your graph from question 4, describe if the average rate of change is increasing or decreasing, from left to right. Justify your observations by comparing the slopes calculated between at least three different pairs of points.

Answer 2

Hey, Hedgie, Are you in an algebra class (where you show up in person) or are you taking an online course?

I ask because these forms of quadratic equations are very common and there should be a table of them in your textbook, if you have a textbook.

I'm sure you must know something about these matters. Mind showing us what you've already done?

I'd be happy to give you one example: a "difference of two squares" could be written as \[a ^{2}-b ^{2}.\]

Answer 3

First we find the square of a, then the square of b, and then we find the difference of the two squares. This is an example of what you're being asked to do.

Answer 4

A better example, one written in terms of x, would be \[f(x)=x ^{2}-a ^{2}, \]
which is now dependent on x as required by the problem statement. Consider a to be a constant, whereas x is a variable.

Answer 5

Well, um, to answer your question, I do school online, and I'm very stupid when it comes to math. My brain just doesn't operate that way. My brain doesn't register how to do all these equations and stuff.

Answer 6

Dear Hedgie: Try to be more positive about your abilities. Home schooling is challenging in that you sometimes have to find your own resources, among other factors. Do you have a textbook? If so, have you looked up "quadratic equations" or "special products and factoring" in that book? If not, you could do an Internet search for the same topics.

It's essential that you have examples to learn from.

"The function h(x) is a perfect square trinomial."
Let me cough up an example of a binomial: x+3.
Supposing that we square this, we get the "perfect square trinomial" \[(x+3)^{2}=(x+3)(x+3)=x ^{2}+6x+9.\]
This last result IS a perfect square trinomial.

Mind starting on the next problem?

Answer 7

No, we don't have text books. Everything is online. The lessons are confusing for me, they don't really make sense, in my head. And I am positive about my abilities, except with math like this. I fail at math, quite litterally. .-.

Alright, so, next one in that list is.. "The function f(x) is a difference of squares."
So.. For that one, creating an equation of my own..
\[f(x) = 2x ^{2} - x^{2}\]

Would that work..? Just checking before I try to work it.

Answer 8

Thanks for trying something on your own; that's really important.
You've written f(x) = 2x^2-x^2. Notice that this can be factored: (x^2) (2-1) = x^2.

If we wrote instead, f(x) = 2a^2-x^2, this would be a better example of "the difference of two squares."

f(x)=4a^2-x^2 would be even better, because 4a^2 is an easy square whose square root is 2a.

Thus, this f(x)=(2a)^2-x^2=(2a-x)(2a+x).

Hope we can talk more about your experience with this online course. I'm interested in what your perceptions of it are and in discussing ways to overcome some of the obstacles you're experiencing.

Answer 9

You were not asked to factor your quadratic expression, but sooner or later you'll encounter factoring and have to do it.

Answer 10

I'm taking Algebra 2, but it's almost the end of the semester, and I'm redoing assignments I did bad on. I'm already past factoring, but.. I suck at math, and can't remember anything from it, so. .-. I appreciate you trying to help me, I really need it. If I don't pull my grade up, I'll fail Algebra 2 and have to graduate late because of redoing the first semester. :( (I'm in 12th grade)

Answer 11

2.Given the function k(x) = x2, compare and contrast how the application of a constant, c, affects the graph. The application of the constant must be discussed in the following manners: •k(x + c)
•k(x) + c
•k(cx)
•c • k(x)

This seemed ambiguous at first. Then I realized that we're given
four different situations and are expected to compare and contrast what each "application" of c means.

We'll really need to do appropriate Internet searches to find examples and explanations.

I can easily start you out, however.

"In comparison to the graph of k(x)=x^2, the graph of k(x) + c has the exact same shape (comparison), but is the graph of k(x) shifted UPWARD by c units (contrast)."