quadratic functions grade 11 applied math

Question

A ball gets kicked from the ground, and the equation that models the height of the ball (measured in metres) versus time (measured in seconds) is given by h(t) = -4.9t2 +12.8t.

How long is the ball in the air, to 2 decimal places, before it hits the ground?

What is the maximum height of the ball to 2 decimal places?

Marks may be awarded as outlined below. If your teacher plans to use a different strategy to evaluate your work they will inform you before you start the assignment.
Unless you are instructed differently this assignment is worth 7 marks. Use the following information to guide your work:

2 marks for calculating the correct x-intercepts
1 marks for showing appropriate work to find the x-intercepts
1 mark for calculating the time the ball is in the air
1 mark for showing appropriate work to find the max height
1 mark for finding the maximum height
1 mark for graphing the quadratic function
Save your work using the following filename:

Answer 1

h(t) = -4.9t^2 + 12.8t;  h(t) = 0 = (-4.9t + 12.8)t;  then:  t = 0 (to start); and -4.9t + 12.8 = 0 (to finish); 

 

then: t = 12.8/4.9 = 2.6122449 sec = 2.61 sec

 

note:  V_0y = 12.8; also:  [V(y)]^2 = [V_0y]^2 - 2(9.8)H;  at top of flight path: V(y) = 0;  then:  0 = 12.8^2 - 2(9.8)H

 

or:  H = 12.8^2/19.6 = 8.36 meters