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## anonymous one year ago For the graph below, what should the domain be so that the function is at least 200? graph of y equals minus 2 times the square of x plus 30 times x plus 200 −5 ≤ x ≤ 20 0 ≤ x ≤ 15 x ≥ 0 All real numbers

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1. anonymous
2. anonymous

@Michele_Laino

3. Michele_Laino

hint: from your graph, I see that: f(0)= 200, f(15)=200, and fo r all point x between 0 and 15, is f(x)>200

4. Michele_Laino

oopss. for all points*

5. anonymous

I am sorry i am still confused.

6. Michele_Laino

|dw:1440187581388:dw|

7. anonymous

Okay.

8. Michele_Laino

at x=0, f(x) = 200 right?

9. anonymous

Right.

10. Michele_Laino

furthermore also at x=15, f(x)= 200

11. anonymous

Okay :]

12. Michele_Laino

and if x>0 and x<15, f(x) is > 200

13. anonymous

0 ≤ x ≤ 15

14. Michele_Laino

yes!

15. anonymous

Is that all for my answer?

16. Michele_Laino

yes!

17. anonymous

Can you help with 1 more? The following graph shows the functions f(x) and g(x): graph of function f of x equals x squared and graph of function g of x equals x squared plus 5 The function g(x) is obtained by adding _______ to f(x). (only input integers) Numerical Answers Expected! Answer for Blank 1:

18. Michele_Laino

we have: $\Large \begin{gathered} f\left( x \right) = {x^2} \hfill \\ g\left( x \right) = {x^2} + 5 \hfill \\ \end{gathered}$

19. Michele_Laino

now I replace x^2 with f(x) into the expression for g(x), and I can write this: $\Large g\left( x \right) = f\left( x \right) + 5$

20. Michele_Laino

so what can you conclude?

21. anonymous

Sorry i am confused.

22. Michele_Laino

the expression of f(x) and g(x) are correct, right?

23. Michele_Laino

expressions*

24. anonymous

Yes?

25. Michele_Laino

ok! now I can rewrite the first equation as below: $\Large {x^2} = f\left( x \right)$

26. anonymous

ok.

27. Michele_Laino

then, I replace x^2 with f(x), into the expression for g(x), so I get this equation: $\Large g\left( x \right) = f\left( x \right) + 5$

28. anonymous

Okay :]

29. Michele_Laino

ok! now, the geometrical meaning of that equation is: |dw:1440188519007:dw|

30. Michele_Laino

|dw:1440188632785:dw|

31. Michele_Laino

so, what is the requested number?

32. anonymous

5?

33. Michele_Laino

correct! since the graph of g(x), as you can see from my drawing, it is shifted up by 5 units with respect to the graph of f(x)

34. anonymous

Thank you!!!!!!!

35. Michele_Laino

:)

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