Web Analytics
Answered

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

Verified Answer :

Answer:

\(0\leq x\leq 15\)

Step-by-step explanation:

Given is the graph with equation

\(y=-2x^2+30x+200\)

This should be atleast 200 implies\(-2x^2+30x+200\geq 200\\x(-2x+30)\geq 0\)

This is the product of two numbers hence would be positive only if either both are positive or both are negative

Case I: Both positive .

\(x\geq 0 and -2x+30\geq 0\\0\leq x\leq 15\)

Case II: Both negative

Then we get

\(x\leq 0 and -2x+30\leq 0\\\\x\leq 0 and x\geq 15\)

This is inconsistent as a value cannot be less than 0 and greater than 15

So solution is

\(0\leq x\leq 15\)

Nerfwolf33445

0 is less than or equal to x is than or equal to 15, B is the correct answer!