Question

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

Answer 1

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

Answer 2

`0\leq x\leq 15`

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`