00:01
For this problem, we're given a quadratic and we want to find the maximum height.
00:05
Now, we know that the maximum height is always going to occur at the vertex.
00:11
So my goal here is to find the vertex.
00:14
In order to find the vertex, i'm going to do a process called completing the square.
00:19
In order to complete the square, i first need to factor out the coefficient of the quadratic term.
00:26
In this case, that's going to be negative 16.
00:28
So when i factor out a 16, i'm left with t squared plus 40, excuse me, minus 40 over 16 t, minus 50 over 16.
00:48
I can simplify those two fractions to give me minus 5 over 2t minus 25 eighths.
01:03
Now in order to complete the square, i next need to group together the first two terms in my parentheses.
01:16
Then inside the parentheses, i'm going to add a constant c.
01:25
And i'm going to subtract c outside the parentheses to make sure my equation remains balanced.
01:34
To find what c equals, i use the formula b over 2 squared, where b is the code.
01:40
Coefficient of the linear term.
01:44
So that gives me a negative five halves over two quantity squared, which equals negative five over four squared, which is 25 sixteenths...