MATH SOLVE

4 months ago

Q:
# The function f(x) = –x2 − 2x + 15 is shown on the graph. What are the domain and range of the function? The domain is all real numbers. The range is {y|y < 16}. The domain is all real numbers. The range is {y|y ≤ 16}. The domain is {x|–5 < x < 3}. The range is {y|y < 16}. The domain is {x|–5 ≤ x ≤ 3}. The range is {y|y ≤ 16}.

Accepted Solution

A:

Answer:The domain is all real numbers. The range is {y|y ≤ 16}.Step-by-step explanation:The vertex of a parabola is given by [tex](\frac{-b}{2a}, \frac{4ac-b^2}{4a})[/tex]. As a = -1, b = -2, c= 15 here, then the vertex is at (1,16).As a is negative, it opens downward, so the range is {y|y ≤ 16}.Meanwhile, all parabolic functions have a domain of [tex]\mathbb{R}[/tex].