Question

help with functions & factoring & graphs?! alg 2.

Answer 1

ive already did the assignment, but my teacher sent it back saying i did parts of it wrong.

Answer 2

Post the question

Answer 3

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.


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)


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.
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.
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 4

& i put 1:
The function f(x) is a difference of squares. y = x^2-9
The function g(x) is a sum of squares. y = x^2 + 9
The function h(x) is a perfect square trinomial. y = x^2 6x 9
The function j(x) can only have a GCF factored out of it. y = x^2 2x


2:


k(x + c)
Shifts the graph horizontally.
If c > 0 , the graph shifts to the left.
If c < 0 , the graph shifts to the right.
If c = 0 , the graph remains unchanged.

k(x) + c
Shifts the graph vertically.
If c > 0 , the graph shifts upwards.
If c < 0 , the graph shifts downwards.
If c = 0 , the graph remains unchanged.

k(cx)
If k(x) = x²
then
k(cx) = (cx)² = c²x²
If c = 0 , the function becomes the trivial function (line) y = 0 .
If c is either positive or negative, c² > 0 , but it depends on what the absolute value of c is as to how it affects the graph of x².
If |c| < 1 , the graph will be stretched vertical and horizontal.
If |c| > 1 , the graph will be compressed vertical and horizontal.

c • k(x)
If c = 0 , the function becomes the trivial function (line) y = 0 .
If 0 < c < 1 , the graph will be stretched vertically and horizontally.
If c > 1 , the graph will be compressed vertically and horizontally.
If -1 < c < 0 , the graph will be reflected across the x-axis, and stretched vertically and horizontally.
If c < -1 , the graph will be reflected across the x-axis, and compressed vertically and horizontally.



3:

a^2 b + c^2 d - abc - acd

a^2 b - abc + c^2 d - acd

ab(a - c) + cd(a - c)

(ab + cd)(a - c)


4: x^2-9

Answer 5

& The equation is f(x)= x^2-9. For finding the x intercepts, you put f(x) equal to zero and find out the values of x. these are x=3 and -3. Find the y intercept, you'll get y=-9

The equation of quadratic equation is ax^2+bx+c. if a>0,the graph is an upward parabola. For this equation, the graph is an upward parabola. The roots of an equation are given by -b+sqrt(b^2-4ac)/2a and -b-sqrt(b^2-4ac)/2a. This one, is b=0.therfore we have real and equal roots of opposite sign(3and-3)

5: Move from left to right. Going from -3 to 0, f(x) is decreasing as you move from x=-3 to x=0. So the slope in this interval is negative. In contrast, when you move from x=0 to x=3, f(x) increases and the slope is positive.

Answer 6

my graph was

Answer 7

& my teacher said "Good job on the quiz! If you would like to review any of the ones you got wrong let me know. Below are some hints to help you with corrections.

#1 actually show how you would factor each if possible. Also on the last two you are missing + and - symbols, please add so we can grade accurately [-5pts]

#2 Please put these all in your words, what you have is correct but it has to all be written in your own words so we know you understand what all that means. [-10pts]

#3 You are missing all of the written explanation of how you did factor and why it is preferred over other methods. Please also make sure you example is unique (one you created and not pulled from the lesson) [-4pts]

#4 Please add these other key features: axis of symmetry, vertex, domain and range
[-7pts]

#5 How do we find rate of change? What is rate of change? In lesson 3.04 page 6 You Try 3 is an example of rate of change. [-4pts] "

Answer 8

ik its a lot but if you could help me id be so thankful!

Answer 9

downloading it

Answer 10

@Nurali @undeadknight26

Answer 11

Scary...next time just post one at a time please :D

Answer 12

it is one at a time lolllll its like one whole thing

Answer 13

come on youre smart help me:(((

Answer 14

lol i already have the first question can you help me with the second?

Answer 15

this one?
2:


k(x + c)
Shifts the graph horizontally.
If c > 0 , the graph shifts to the left.
If c < 0 , the graph shifts to the right.
If c = 0 , the graph remains unchanged.

k(x) + c
Shifts the graph vertically.
If c > 0 , the graph shifts upwards.
If c < 0 , the graph shifts downwards.
If c = 0 , the graph remains unchanged.

k(cx)
If k(x) = x²
then
k(cx) = (cx)² = c²x²
If c = 0 , the function becomes the trivial function (line) y = 0 .
If c is either positive or negative, c² > 0 , but it depends on what the absolute value of c is as to how it affects the graph of x².
If |c| < 1 , the graph will be stretched vertical and horizontal.
If |c| > 1 , the graph will be compressed vertical and horizontal.

c • k(x)
If c = 0 , the function becomes the trivial function (line) y = 0 .
If 0 < c < 1 , the graph will be stretched vertically and horizontally.
If c > 1 , the graph will be compressed vertically and horizontally.
If -1 < c < 0 , the graph will be reflected across the x-axis, and stretched vertically and horizontally.
If c < -1 , the graph will be reflected across the x-axis, and compressed vertically and horizontally.

Answer 16

yeaa:( could you help me put that into my own words? my teacher said that the information is right, but it has to be in my own words

Answer 17

:O if i put it in my words then you would have to reword that to make it into your own words...

Answer 18

I KNOW. but like idkk how

Answer 19

lol nvm thanks anyways.