Determine the domain and range of the quadratic function. (enter your answers using interval notation.) f(x) = −4(x + 1)2 − 4

Domain -∞ < x < +∞

Range f(x) ≤ - 4

Step-by-step explanation:

The given quadratic function is f(x) = - 4 (x + 1)² - 4

Now, we have to find the domain and range of the quadratic function.

Now, it is clear from the given function that f(x) will have real value for all real value of x.

Therefore, the domain of the function is -∞ < x < +∞ (Answer)

Now, (x + 1)² is always ≥ 0

i.e. (x + 1)² ≥ 0

⇒ - 4 (x + 1)² ≤ 0 {Since the inequality sign changes for multiplying both sides of the equation by a negative term}

⇒ - 4 (x + 1)² - 4 ≤ - 4

⇒ f(x) ≤ - 4

Therefore, this is the required range of the function f(x). (Answer)

i = 2 / - 5

step-by-step explanation:

evaluation of ( 2 - 4 ) ( p + q ) when p = 2 and q = 5 i, by putting values of p and q,                                                                    

step-by-step explanation:

12: 00 p.m. to 7: 00 p.m. is a total of 7 hours.

4: 00 p.m. to 7: 00 p.m. is a total of 3 hours.

this means that from 4: 00 p.m to 7: 00 p.m. this represents 3/7 of what was lost from 12: 00 p.m. to 7: 00 p.m.

after knowing this, after doing 11,600 - 6,800 = 4,800

4,800 represents 3/7 of what was lost for 7 hours.

we then divide 4,800 by 3 which gets 1,600.

because we know that 1,600 represents 1/7 of how much water was lost, we just have to multiply by 7, which gets 11,200.   after adding 11,200 to how much water was left at 7: 00 p.m. which was 6,800. 11,200 + 6,800 = 18,000

this means that the pool originally had 18,000 gallons in the pool.

you can also check your work by doing 18,000 - 4(1600), which becomes           1800 - 6400 which gets you 11,600.