A teenager who is 5 feet tall throws an object into the air. The quadratic function f(x)=−16x2+64x+5 ( ) = − 16 2 + 64 + 5 is where f(x) ( ) is the height of the object in feet and x is the time in seconds.
Since the function f(x) represents the height of the object in feet, we can plug in the time in seconds to find out how high the object is at that specific time.
If we plug in x = 0 into the function f(x), we can find out the initial height of the object.
f(0) = −16(0)^2 + 64(0) + 5
f(0) = 5
This means that the initial height of the object is 5 feet.
To find out the maximum height the object reaches, we need to find the vertex of the parabola represented by the quadratic function.
The x-coordinate of the vertex can be found using the formula -b/2a, where a = -16 and b = 64.
x = -64 / 2(-16) = -64 / -32 = 2
Plugging in x = 2 into the function f(x) will give us the maximum height of the object.
f(2) = -16(2)^2 + 64(2) + 5
f(2) = -16(4) + 128 + 5
f(2) = -64 + 128 + 5
f(2) = 69
Therefore, the maximum height the object reaches is 69 feet.