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Eva is jumping on a trampoline. Her height h at time t can be modeled by the equation h=-16t^2+20t+6. Would Eva reach a height of 14 feet?

Respuesta :

CastleRook
Given the equation modeling Eva's height at time,t. To evaluate if she will reach height of 14 ft, we evaluate maximum height that she will reach.
At maximum height h'(t)=0
but
h(t)=-16t^2+20t+6
h'(t)=-32t+20=0
solving for t we get:
-32t=-20
t=20/32
t=5/8
thus the maximum height reached was:
h(5/8)=-16(5/8)^2+20(5/8)+6
h(5/8)=12.25 ft
Thus we conclude that she won't reach the height of 14 ft because her maximum height was 12.25 ft

A function assigns the value of each element of one set to the other specific element of another set. Eva can not reach a height of 14 feet.

What is a Function?

A function assigns the value of each element of one set to the other specific element of another set.

As the function of the height of the jump, Eva is given as h=-16t^2+20t+6. Now, in order to know if Eva will reach 14 feet height, we need to substitute the value of her height of Eva as 14 feet, therefore,

[tex]h=-16t^2+20t+6\\\\14=-16t^2+20t+6\\\\16t^2 - 20t+14-6=0\\\\16t^2 -20t + 8=0[/tex]

If we calculate the discriminant of the given quadratic equation, we will understand that the given quadratic equation has imaginary roots.

Therefore, Eva can not reach a height of 14 feet.

Learn more about Function:

https://brainly.com/question/5245372

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