Question

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

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

Answer:

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

0 ≤ x ≤ 25

Step-by-step 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