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)

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step-by-step explanation:

m

1

=

5

m1=5

b

=

−

1

b=-1

find the slope and y-intercept of the second equation.

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m

2

=

0

m2=0

b

=

−

6

b=-6

compare the slopes

m

m of the two equations.

m

1

=

5

,

m

2

=

0

m1=5,m2=0

compare the two slopes in the decimal form. if the slopes are equal, then the lines are parallel. if the slopes are not equal, then the lines are not parallel.

m

1

=

5

,

m

2

=

0

m1=5,m2=0