Mathematics, 11.07.2019 03:00, mmmmm96061

Predict the relationship between the graph of y=x^3 - x^2 and the graph of y+3=(x - 2)^3 - (x - 2)^2. graph each function. - , i’m honestly very lost. i’ve attached a photo to you see the question better too.

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Answers

answered: jaylen63

Remark

If you start with the graph y = x^3 - x^2, it will cross the x axis at (0,0). The y intercept for that graph is when x = 0. Thus y = 0^3 - 0^2 = 0 when x = 0 and that 's how you derive (0,0)

Remark 2

Now watch that point (0,0) on the left graph below when you change it to y = (x - 2)^3 - (x - 2)^2 [Never mind the 3 for now. We'll deal with it later on]. Notice that what is happening at (2,0) is what is happening with the blue graph as compared to the red one. The change is very dramatic. Instead of going up, both graphs start to go down at the points I'm telling you to watch.

Conclusion 1.

So the first prediction you should make is that the - 2 forces the graph to move 2 units to the right.

Remark 3

What about the three on the right hand side? It is easier if you rewrite the equation as y = (x-2)^3 - (x -2)^ - 3. That means you have subtracted three from the right side. That should move (2,0) down 3 units. (minus is down when a number is on the right.) The green line in the right graph shows you that.

Conclusion 2

The green line shows you the final movement. (0,0) goes 3 units down and 2 units right. The new point we have been watching is (2,3)

Predict the relationship between the graph of y=x^3 - x^2 and the graph of y+3=(x - 2)^3 - (x - 2)^2

answered: Guest

$a_1 = 1$ , and

$a_{n+1} = a_n + (n + 1)$ for $n \ge 1$

step-by-step explanation:

we can analyze the pattern at which the terms increase. let us denote $a_1 = 1$ , $a_2 = 3$ , $a_3 = 6$ , so that we can call

1 the 1st term, 3 the 2nd term, 6 the 3rd term,etc.

note the following:

from the 1st term (1) to the 2nd term (3), we go up by 2,from the 2nd term (3) to the 3rd term (6), we go up by 3from the 3rd term (6) to the 4th term (10), we go up by 4, andfrom the 4th term (10) to the 5th term (15), we go up by 5.

the pattern: to get the next term value, we just add the next term number (e.g. 1st, 2nd, to the previous term value (term values are the given numbers in the question, 1, 3, 6, 10, 15,

from $a_1 = 1$ , to get to $a_2 = 3$ , we add $2(=1+1)$

from $a_2 = 3$ , to get to $a_3 = 6$ , we add $3 (=2+1)$

etc.

we need to form a recursive formula, a formula that has the next term as a function of the previous term. so a possible recursive formula can be

$a_1 = 1$ , and $a_{n+1} = a_n +(n + 1)$ for $n \ge 1$

answered: Guest

50-60=10

step-by-step explanation:

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Predict the relationship between the graph of y=x^3 - x^2 and the graph of y+3=(x - 2)^3 - (x - 2)^2...