a water balloon was thrown from the window. The height of the water balloon over time can be modeled by the function y=-16square2+160x+50

The maximum height of the water balloon : 450 m

Quadratic function is a function that has the term x²  

The quadratic function forms a parabolic curve  

The general formula is  

f (x) = ax² + bx + c  

where a, b, and c are real numbers and a ≠ 0.  

The parabolic curve can be opened up or down determined from the value of a. If a is positive, the parabolic curve opens up and has a minimum value. If a is negative, the parabolic curve opens down and has a maximum value  

So the maximum is if a <0 and the minimum if a> 0.  

The formula for finding the coordinates of the maximum and minimum points of the quadratic function is the same.  

The maximum / minimum point of the quadratic function is  

Where  

D = b²-4ac  

The function h (t) = -16x²+160x+50

so the value of a <0, then it has a maximum value  

Because we are looking for maximum height, then we find the value of the y coordinate, with the formula  

Questions we might add :

What was the maximum height of the water balloon after it was thrown?

We can also use the first derivative of the above function to find the maximum value

input to function :

1. x> -5

2. x< 8

step-by-step explanation:

1. 2x> -10

divide by 2 from both sides of equation.

2x/2> -10/2

simplify, to find the answer.

-10/2=-5

x> -5 is the correct answer.

2. 3x< 24

divide by 3 from both sides of equation.

3x/3< 24/3

simplify, to find the answer.

24/3=8

x< 8 is the correct answer.

i hope this you, and have a wonderful day!