WEBVTT

1
00:00:00.000 --> 00:00:08.720
For times from zero to six, the height model is negative two t squared plus twelve t plus five.

2
00:00:08.920 --> 00:00:13.080
We need the maximum height, not the time when it occurs.

3
00:00:13.280 --> 00:00:17.760
The negative leading coefficient makes the parabola open downward.

4
00:00:17.960 --> 00:00:25.080
The vertex time is negative b divided by two a: negative twelve divided by negative four, or three.

5
00:00:25.269 --> 00:00:32.469
Substitute three into the original model: negative eighteen plus thirty six plus five equals twenty three.

6
00:00:32.669 --> 00:00:37.869
The maximum height is twenty three meters. Three is the time, not the height.

7
00:00:38.026 --> 00:00:45.186
Completing the square gives negative two times the quantity t minus three squared, plus twenty three.

8
00:00:45.386 --> 00:00:55.346
That negative square cannot be positive. The vertex is permitted, and both endpoints have height five, confirming the maximum of twenty three.