Answer:
Domain: All real numbers
Range: f(x) ≥ - 11
Step-by-step explanation:
Given the quadratic function in vertex form, f(x) = ½(x + 4)² - 11:
The vertex, (h, k) is (-4, -11).
<h3 /><h3>Range:
f(x) ≥ -11. </h3>
The parabola opens upward (where <em>a</em> = ½, which is greater than 0), and <em>k</em> = -11 is the minimum value for f(x). Hence, the range of the given function must be <u>at least</u> -11, or f(x) ≥ -11.
<h3 /><h3>Domain:
all real numbers</h3>
There is no restriction for the value of <em>x. </em>Therefore, the <u>domain</u> of the given function is all real numbers.
