Question

For the graph below, what should the domain be so that the function is at least 300?

graph of y equals minus 2 times the square of x plus 50 times x plus 300

x _ 0

-5 _ x _ 30

0 _ x _ 25

all real numbers

Answer 1

y = -2x^2 + 50x + 300
-2x^2 + 50x + 300 ≥ 300
-2x^2 + 50x ≥ 0
-2x^2 ≥ -50x
x^2 ≤ 25x
x ≤ 25

Therefore, required domain is 0 ≤ x ≤ 25

Answer 2

The domain of the function so that the function is at least 300 is:

0 ≤ x ≤ 25

Explanation:

We are given graph of the function y as:

`y =-2x^2+50x+300`

`-2x^2+50x+300\geq 300`

on subtracting both side of the inequality by 300 we obtain:

`-2x^2+50x\geq 0`

`-2x(x-25)\geq 0`

This inequality is obtained when one of the term is positive and the other is negative:

i.e. if x≥0

and x-25≤0

i.e. x≤25 then the product :

-2x(x-25)≥0.

Hence, the domain is:

0 ≤ x ≤ 25