A rocket goes into teh air and its path is represented by the following function in t seconds and h meters: h=3t2+6t+27

Question

h=3t²+6t+27

Answer 1

It seems like you want to complete the square. First, factor out a 3 and divide to get it on the other side. Subtract that 9 from both sides to move it as well:

 

h = 3(t² + 2t + 9)

h/3 = t² + 2t + 9

h/3 - 9 = t² + 2t

 

To complete the square, you need to add some constant to both sides so that the right-hand side is a perfect square. That means the constant needs to be (b/2)² = (2/2)² = 1² = 1. Add one to both sides and factor the right-hand side:

 

h/3 - 8 = t² + 2t + 1

h/3 - 8 = (t + 1)(t + 1)

h/3 - 8 = (t + 1)²

 

You've completed the square! Now let's move the 8 and 3 back over by adding 8 and then multiplying by 3:

 

h/3 = (t + 1)² + 8

h = 3(t + 1)² + 24