answer to this application question needed ASAP PLEASE

Question

a video tracking device recorded the height, h in metres, of a baseball after it was hit into the air. the data collected can be modelled by the quadratic relation h=-3(t-3)^2+18. where t is the time in seconds after the ball was hit.

A) what was the maximum height reached by the baseball

b) when did the baseball reach its maximum height

c) at what time(s) was the baseball at a height of 10m

d) approximately what height did the baseball hit the ground

Answer 1

A) 18 meters

B) In 3 seconds

C) In 3 ±√8/3 seconds the height is 10

3 + √8/3 = t = 4.63299 seconds and h is10

3 - √8/3 = t = 1.36700 seconds and h is 10

D) Do you mean at what time, t because height is 0 when the ball is on the ground

the time when the ball returns to the ground is about 3 + √6 = 5.449 seconds

For

h=-3(t-3)^2+18

h = -3(t - 3)² + 18

h = -3(t² - 6t + 9) + 18

h = -3t² + 18t - 27 + 18

h = -3t² + 18t - 9

Is a parabola that opens downward

A and B can be found by setting the first derivative equal to 0

The first derivative is

-6t + 18

0 = -6t +18

6t = 18

t = 18/6

t = 3

(t, h) t is 3 seconds, h is 18 meters (3, 18) this is a maximum

C)To find out when the ball is 10 meters high

Set h = 10 and solve for t as follows, use the original equation

10 = h = -3(t - 3)² + 18

10 = -3(t - 3)² + 18

Subtract 18 from both sides of the equation

-8 = -3(t - 3)²

Divide both sides by negative 3

-8/-3 = (t - 3)²

8/3 = (t -3)²

Take the square root of both sides of the equation

√8/3 = t - 3

3 + √8/3 = t = 4.63299 seconds and h is 10

3 - √8/3 = t = 1.36700 seconds and h is 10

To find out when about when the ball is on the ground, set h =0 in the original equation and solve for t

h = -3(t - 3)² + 18

0 = -3(t - 3)² + 18

Divide both sides of the equation by -3

0 = (t - 3)² - 6

Add 6 to both sides if the equation,

6 = (t - 3)²

Take the square root of both sides

√6 = t - 3

Solve for t by adding 3 to both sides

3 ±√6 = t

You can check with the original equation and you can graph your function at Desmos.com

Or

You can also confirm the vertex with -b/2a for

h = -3t² + 18t - 9

b = 18

a = -3

-b/2a = -18/2(-3) = -18/-6 = 18/6 = 3

h = -3(3)² + 18(3) - 9

h = -27 + 54 - 9

h = 18

Give it a try