An object is thrown vertically so that its height in feet above the ground x seconds after it is thrown can be found
using the following quadratic function
f(x)=-16x^2+64x+80
h = -16x^2 + 64x + 80 = 0
Use Quadratic Formula.
X = -1, and 6.
Select the positive value:
X = 6 s. = Time to reach gnd.
To find the height of the object at any given time, we need to use the function f(x) = -16x^2 + 64x + 80. This function is a quadratic function in the form of f(x) = ax^2 + bx + c, where a, b, and c are coefficients.
The coefficient -16 represents the acceleration due to gravity. Since gravity pulls objects downwards, the coefficient is negative (-16). The term -16x^2 represents the downward acceleration of the object.
The term 64x represents the initial vertical velocity of the object. It tells us how fast the object is initially moving upwards or downwards.
The constant term 80 represents the initial height of the object when it is thrown. It is the height above the ground at x = 0 (initial time).
To find the height above the ground at a specific time, substitute the value of x into the function f(x).
For example, if you want to find the height of the object after 2 seconds, substitute x = 2 into the function f(x):
f(2) = -16(2)^2 + 64(2) + 80
= -16(4) + 128 + 80
= -64 + 128 + 80
= 144
Therefore, the object will be at a height of 144 feet above the ground after 2 seconds.
You can use the same approach to find the height at any other specific time by substituting the value of x into the function f(x).