Mishita Dharia - Quadratics

The height of a baseball is thrown from the top of a building and can be approximated by the formula h= -2t^2 + 6t + 36, where t is the time in seconds and h is the height in metres.

 

a) Write the formula in factored form

h= -2t^2 + 6t +36 [take out the common factor]

h = -2[t^2 - 3t – 18] [Find the factors that multiply to get the product of -18, and                                       add together toget a sum of -3]

(-6)x(3) = -18

(-6)+(3) = -3

 

h = -2[t^2 - 3t – 18]

h = -2(t-6)(t+3)

 

b) When will the ball hit the ground? [find the zeros]

h = -2(t-6)(t+3)

 

 

 

t - 6 = 0    

t = 6          

 

The ball will hit the ground at 6 seconds.

 

c) What is the maximum height the ball will reach in metres? [maximum height/vertex]

A.O.S = [6 + (-3)]/2

A.O.S = 3/2

A.O.S = 1.5

 

h = -2t^2 + 6t + 36

h = -2(1.5)^2 + 6(1.5) + 36

h =-4.5 + 9 + 36h = 40.5

 

Therefore the maximum height is 40.5m.