x^2 + 8x = -3
x^2 + 8x + 16 = -3 + 16
using a^2 + 2 a b + b^2 = (a+b)^2

x^2 + 8x + 16 = 13

(x +4)^2 = 13

answer : 16 is the number you must add to complete the square

5 0

3 years ago

A food packet is dropped from a helicopter and is modeled by the function f(x) = −15x2 + 6000. The graph below shows the height

melisa1 [442]

General Idea:

Domain of a function means the values of x which will give a DEFINED output for the function.

Applying the concept:

Given that the x represent the time in seconds, f(x) represent the height of food packet.

Time cannot be a negative value, so

$x\geq 0$

The height of the food packet cannot be a negative value, so

$f(x)\geq 0$

We need to replace $-15x^2+6000$ for f(x) in the above inequality to find the domain.

$-15x^2+6000\geq 0 \; \; [Divide \; by\; -15\; on\; both\; sides]\\ \\ \frac{-15x^2}{-15} +\frac{6000}{-15} \leq \frac{0}{-15} \\ \\ x^2-400\leq 0\;[Factoring\;on\;left\;side]\\ \\ (x+200)(x-200)\leq 0$

The possible solutions of the above inequality are given by the intervals $(-\infty , -2], [-2,2], [2,\infty )$ . We need to pick test point from each possible solution interval and check whether that test point make the inequality $(x+200)(x-200)\leq 0$ true. Only the test point from the solution interval [-200, 200] make the inequality true.

The values of x which will make the above inequality TRUE is $-200\leq x\leq 200$

But we already know x should be positive, because time cannot be negative.

Conclusion:

Domain of the given function is $0\leq x\leq 200$

4 0

3 years ago

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