Question 258057
We can find the maximum height by completing the square.
step 1 - rewrite the equation as
{{{-16t^2 + 45t + ____ + 40 + ____}}}
The blanks are waiting for numbers.
step 2 - factor out a -16 only from the first two parts to get
{{{-16(t^2 - (45/16)t + _____ ) + 40 + _____}}}
step 3 - take 1/2 of the middle term and square it as
{{{-16(t^2 - (45/16)t + (-45/32)^2 ) + 40 + _____}}}
step 4 - multiply this squared answer by -16 to get 31.64. place this number in the second blank to get
{{{-16(t^2 - (45/16)t + (-45/32)^2 ) + 40 + 31.64}}}
step 5 - rewrite the trinomial as a binomial squared and simplify as
{{{-16(t-(45/32))^2 + 71.64}}}
Now, the max ht occurs at 45/32 seconds @ 71.64 ft.