A portion of the graph of f(x) = −x2 − 2x + 8 is shown. Which of the following describes all solutions for f(x)?

a partial parabola opening down and passing through negative 4 comma 0 and 2 comma zero with endpoints at negative 5 comma negative 7 and 3 comma negative 7

(x, −x2 − 2x + 8), where −5 ≤ x ≤ 3
(x, y), where −4 ≤ x ≤ 2
(x, −x2 − 2x + 8), where −4 ≤ x ≤ 2
(x, y) for all real numbers

where −5 ≤ x ≤ 3

Step-by-step explanation:

The given function is .

We want to select the option that describes all the solutions to the parabola.

The domain of the parabola is −5 ≤ x ≤ 3.

This means that  any x=a on −5 ≤ x ≤ 3 that satisfies (a,f(a)), is a solution.

This can be rewritten as

Therefore for x belonging to −5 ≤ x ≤ 3, all solutions are given by:

where −5 ≤ x ≤ 3.

560

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