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Tosha is trying to find the solution(s) to the system {f(x)=x3−3x2+2g(x)=−x2+x.
After analyzing the graph of the functions, Tosha comes up with the following list of ordered pairs as possible solutions: (−1,−2), (0,0), (1,0), and (2,−2).
Part A: Which method should Tosha use to determine which of the ordered pairs are solutions to the system of equations?
Part B: What are the solutions to the system?
Select one answer for Part A, and select all answers that apply for Part B.
A: Tosha must verify each solution individually. For (−1,−2), she should evaluate f(−2) and g(−2). If she gets −1 as the result in both cases, then (−1,−2) is a solution of the system. She will test each of the other ordered pairs in the same way.
B: (0,0)
B: (2,−2)
A: Tosha must verify each solution individually. For (−1,−2), she should evaluate f(−1) and g(−2). If f(−1)=−2 and g(−2)=−1 then (−1,−2) is a solution of the system. She will test each of the other ordered pairs in the same way.
A: Tosha must verify each solution individually. For (−1,−2), she should evaluate f(−1) and g(−1). If she gets −2 as the result in both cases, then (−1,−2) is a solution of the system. She will test each of the other ordered pairs in the same way.
B: (−1,−2)
A: Tosha must verify each solution individually. For (−1,−2), she should evaluate f(−2) and g(−1). If f(−2)=−1 and g(−1)=−2 then (−1,−2) is a solution of the system. She will test each of the other ordered pairs in the same way.
B: (1,0)
A: Tosha can verify whether these ordered pairs are solutions by zooming in on the graph at each ordered pair to determine whether it is a solution.
I have tried multiple options and have got it incorrect I seem to be lost. If you can help it would be greatly apprieted
Not sure of your typing, I will assume you have:
f(x)=x^3−3x^2+2
g(x)=−x^2+x
So rather than all that wordage morass , why not just solve the system?
x^3−3x^2+2 = −x^2+x
x^3 + 2x^2 - x + 2 = 0
let's plot my interpretation:
https://www.wolframalpha.com/input/?i=plot+%E2%88%92x%5E3%2B3x%5E2+%3D%E2%88%92x%5E4%2B5x%5E3%E2%88%926x%5E2%2B3+
clearly, none of the answers found by Tosha will work, so you must mean something else.
You start with { but never close it.
Is f(x) = x^3−3x^2+2g(x) , where g(x) = −x^2+x
then you would simply have
f(x) = x^3−3x^2+2(−x^2+x)
and now you have a single function which looks like this:
https://www.wolframalpha.com/input/?i=plot+f%28x%29+%3D+x%5E3%E2%88%923x%5E2%2B2%28%E2%88%92x%5E2%2Bx%29+
Again, none of your given answers apply, so ....
check your question
Part A: Tosha must verify each solution individually. For example, for the ordered pair (−1,−2), she should evaluate f(−1) and g(−1). If she gets −2 as the result in both cases, then (−1,−2) is a solution of the system. She will test each of the other ordered pairs in the same way.
Part B: The solutions to the system are:
- (0,0)
- (2,−2)
Of course, I can help you with this problem. Let's break it down step by step:
Part A: To determine which of the ordered pairs are solutions to the system of equations, Tosha needs to evaluate each pair by substituting the values into the equations f(x) and g(x).
Part B: The solutions to the system are the ordered pairs that satisfy both equations, meaning when you substitute the values into both f(x) and g(x), you should get true statements.
Let's go through the options one by one:
Option A: Tosha must verify each solution individually. For example, for the ordered pair (−1,−2), she should evaluate f(−2) and g(−2). If she gets −1 as the result in both cases, then (−1,−2) is a solution of the system. She will test each of the other ordered pairs in the same way.
Option B: (0,0) and (2,−2) are listed as solutions to the system. According to the question, she may have come up with these solutions by analyzing the graph of the functions. However, to be certain, she still needs to verify them by substituting the values into the equations f(x) and g(x). So, (0,0) and (2,−2) need to be tested.
Option A: Tosha must verify each solution individually. For example, for the ordered pair (−1,−2), she should evaluate f(−1) and g(−2). If f(−1)=−2 and g(−2)=−1, then (−1,−2) is a solution of the system. She will test each of the other ordered pairs in the same way.
Option A: Tosha must verify each solution individually. For example, for the ordered pair (−1,−2), she should evaluate f(−1) and g(−1). If she gets −2 as the result in both cases, then (−1,−2) is a solution of the system. She will test each of the other ordered pairs in the same way.
Option B: (−1,−2) and (1,0) are listed as solutions to the system. Again, to be certain, Tosha needs to verify them by substituting the values into the equations f(x) and g(x). So, (−1,−2) and (1,0) need to be tested.
Option A: Tosha must verify each solution individually. For example, for the ordered pair (−1,−2), she should evaluate f(−2) and g(−1). If f(−2)=−1 and g(−1)=−2, then (−1,−2) is a solution of the system. She will test each of the other ordered pairs in the same way.
Option B: (1,0) is listed as a solution to the system. Similarly, Tosha needs to verify it by substituting the values into the equations f(x) and g(x). So, (1,0) needs to be tested.
Option A is the correct answer for Part A because Tosha needs to verify each solution individually by evaluating both f(x) and g(x) for each ordered pair.
For Part B, the correct options are (0,0) and (2,−2) because they are the solutions that satisfy both equations when substituting the values into f(x) and g(x). (−1,−2) and (1,0) need to be verified to confirm if they are solutions to the system as well.
I hope this explanation helps you understand the problem better and identify the correct answers. If you have any more questions, feel free to ask!