Task 1:
Your nephew is standing on his deck, which is 4 feet off the
ground. He fosses his toy up into the air at an initial velocity
of 7 feet per second. The equation h = -212 + 7+ + 4 models
the toy's height hin feet from the ground att seconds after
he threw it.
B: What is the toy's maximum height?
C: How long is the toy in the air?

maximum height is 4.058 metres

Time in air = 0.033 second

Step-by-step explanation:

Given that the equation height h

h = -212t^2 + 7t + 4

What is the toy's maximum height?

Let us assume that the equation is a perfect parabola

Time t at Maximum height will be

t = -b/2a

Where b = 7 and a = - 212

t = -7/ - 212 ×2

t = 7/ 424 = 0.0165s

Substitute t in the main equation

h = - 212(7/424)^2 + 7(7/424) + 4

h = - 0.05778 + 0.115567 + 4

h = 4.058 metres

Therefore the maximum height is 4.058 metres

How long is the toy in the air?

The object will go up and return to the ground.

At ground level, h = 0

-212t^2 + 7t + 4 = 0

212t^2 - 7t - 4 = 0

You can factorize the above equation and pick the positive time t since time can't be negative

Or

Since we have assumed that it's a perfect parabola,

Total time in air = (-b/2a) × 2

Time in air = 0.0165 × 2 = 0.033 s

x=6 and x=3

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