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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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

Mathematics
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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

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Other answers:

oopss. for all points*
I am sorry i am still confused.
|dw:1440187581388:dw|
Okay.
at x=0, f(x) = 200 right?
Right.
furthermore also at x=15, f(x)= 200
Okay :]
and if x>0 and x<15, f(x) is > 200
0 ≤ x ≤ 15
yes!
Is that all for my answer?
yes!
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:
we have: \[\Large \begin{gathered} f\left( x \right) = {x^2} \hfill \\ g\left( x \right) = {x^2} + 5 \hfill \\ \end{gathered} \]
now I replace x^2 with f(x) into the expression for g(x), and I can write this: \[\Large g\left( x \right) = f\left( x \right) + 5\]
so what can you conclude?
Sorry i am confused.
the expression of f(x) and g(x) are correct, right?
expressions*
Yes?
ok! now I can rewrite the first equation as below: \[\Large {x^2} = f\left( x \right)\]
ok.
then, I replace x^2 with f(x), into the expression for g(x), so I get this equation: \[\Large g\left( x \right) = f\left( x \right) + 5\]
Okay :]
ok! now, the geometrical meaning of that equation is: |dw:1440188519007:dw|
|dw:1440188632785:dw|
so, what is the requested number?
5?
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)
Thank you!!!!!!!
:)

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