# 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

**Solution:**

Given: Graph of y equals minus 2 times the square of x plus 50 times x plus 300.

It can be mathematically represented as

y = -2x^{2} + 50x + 300

So we get,

-2x^{2} + 50x + 300 ≥ 300

By subtracting 300 on both sides

-2x^{2} + 50x ≥ 0

Taking 50x on the RHS

-2x^{2 }≥ -50x

Divide both sides by -2

x^{2 }≤ 25x

Divide both sides by x

x ≤ 25

Therefore, the required domain is 0 ≤ x ≤ 25.

## 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

**Summary:**

For the graph below, the domain should be 0 ≤ x ≤ 25 so that the function is at least 300.