Sandy reached for the radio to turn it up louder. (Para. 3)
Meaning: Sandy stretched her hand out to increase the volume of the radio.
reach for: stretch one's hand so as to touch or hold something
In "reach for", "reach" is used as an intransitive verb.
There was no time for me to reach for my gun. 我沒有時間伸手拿槍。
Please notice that the verb "reach" is often used as a transitive verb, meaning
(1) get to, come to, arrive at
You can see the house when you reach the top of the hill. 到了山頂上，你就能看到那座房子了。
Your letter reached me yesterday. 我昨天收到了你的信。
(2) touch, get in touch with
I am short and cannot reach the top of the wall. 我個子矮，摸不到墻頂。
turn up: increase (a flame, a sound, etc.) usually by moving a switch
We turned up the heat to make the room warmer. 我們把暖氣調高使房間更加暖和。