## anonymous one year ago 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.

1. anonymous

@ali2x2

2. Michele_Laino

we can rewrite your parabola as below: $\Large y - 4 = {\left( {x - 2} \right)^2}$

3. Michele_Laino

now, if we make this change of variable: $\Large \left\{ \begin{gathered} Y = y - 4 \hfill \\ X = x - 2 \hfill \\ \end{gathered} \right.$ where X, and Y are the new variables, then your parabola can be rewritten as below: $\Large Y = {X^2}$

4. Michele_Laino

the graph of that parabola is: |dw:1439045316314:dw|

5. Michele_Laino

as we can see the vertex has the subsequent coordinates: X=0 and Y=0, so we can write: $\Large \left\{ \begin{gathered} Y = y - 4 = 0 \hfill \\ X = x - 2 = 0 \hfill \\ \end{gathered} \right.$ so, what are x and y? Furthermore, we note that the range of our parabola is given by the subsequent equation: $\Large Y \geqslant 0$ from which we have: $\Large y - 4 \geqslant 0$ please solve that equation with respect to y, and you will find the requested range