Question

HELP I WILL FAN AND MEDAL
For the function f(x) = (x − 2)2 + 4, identify the vertex, domain, and range.
a) The vertex is (–2, 4), the domain is all real numbers, and the range is y ≥ 4.
b) The vertex is (–2, 4), the domain is all real numbers, and the range is y ≤ 4.
c) The vertex is (2, 4), the domain is all real numbers, and the range is y ≤ 4.
d) The vertex is (2, 4), the domain is all real numbers, and the range is y ≥ 4.

Answer 1

HI!!

Answer 2

\[f(x)=(x-\color{red}h)^2+\color{green}k\] has vertex \((\color{red}h,\color{green}k)\)

Answer 3

The range can be determined by considering whether the graph is concave up or down.
Concave up (when the coefficient of x^2 is positive, implies the graph has a minimum value. Thus the rest of the graph is above this minimum value so the range is given by
\[y \ge y_\min\]
Concave down exact opposite. Coefficient of x^2 is negative, implies the graph has a maximum value. Thus the rest of graph is below this maximum so the range is given by
\[y \le y_\max\]