Question

The height, h, in meters above ground, of a projectile at any time, t, in seconds, after the launch is defined by the

function h(t) = -4t² + 19t +5. The graph is shown below. When rounded to the nearest tenth, what is the
maximum height reached by the projectile, how long did it take to reach its maximum height, and when did the
projectile hit the ground?
+25
+20
-15
-10
Time (sec)
O The projectile reached a maximum height of 26.7 meters in 2.2 seconds and it took 5.0 seconds for it to hit the ground.
O The projectile reached a maximum height of 27.6 meters in 2.4 seconds and it took 5.0 seconds for it to hit the ground.
O The projectile reached a maximum height of 27.2 meters in 2.3 seconds and it took 4.8 seconds for it to hit the ground.
O The projectile reached a maximum height of 2.4 meters in 27.6 seconds and it took 5.1 seconds for it to hit the ground.
h(t) (m)

Answer 1

the projectile reached a maximum height of 27.6 meters in 2.4 seconds and it took 5.0 seconds for it to hit the ground

Explanation:

to find the vertex you can find the axis of symmetry first

that equation is -b/2a

-19/-8 = 2.375

then you take this and plug it in

-4(2.375)^2 + 19*2.375 + 5

that gives you 27.5625

then you have to find when it hits the ground

you can factor to find this out

-4t^2 + 19t + 5

4t^2 - 19t - 5

4t^2 + t - 20t - 5

t(4t + 1) -5(4t +1)

(t - 5)(4t + 1)

t = {5, -1/4}

we can only take positive time so it took 5 seconds

the answer is the second one