For the graph below, what should the domain be so that the function is at least 200?

Asked by maham237 @ 25/12/2020 in Mathematics viewed by 285 People

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

Answered by maham237 @ 25/12/2020

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

$0\leq x\leq 15$

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