For the graph, what is a reasonable constraint 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

The correct constraint is:

0 ≤ x ≤ 15

Step-by-step explanation:

The function given to us in the question is:

y = - 2x² + 30x + 200

It is given that the function is at least 200, we can write is as:

-2x² + 30x + 200 ≥ 200 ⇒ Equation (i)

To find the constraint, replace ≥ sign with = sign and solve for x:

-2x² + 30x + 200 = 200

-2x² + 30x = 0

x (-2x + 30) = 0

x = 0, - 2x + 30 = 0

x = 0, - 2x = - 30

x = 0, x = - 30/-2

x = 0, x = 15

So the end values of constraint are 0 and 15.

Take any value between 0 and 15 and substitute in equation (i) to see whether it satisfies the equation or not.

-2x² + 30x + 200 ≥ 200

Substitute x = 5 in the equation:

-2 (5) ² + 30 (5) + 200 ≥ 200

-50 + 120 + 200 ≥ 200

270 ≥ 200

As the equation satisfies. it means that the solution lies between 0 and 15, including the end values.

Hence.

0 ≤ x ≤ 15