Piper drops her keys from a third-story window to a friend standing on the sidewalk. The distance between the keys and the ground, in feet, can be represented by the function f(x)=-16x^2+32, where x is the time in seconds. Piper would like to be able to determine the time, in seconds, at which the keys were at any distance from the ground. What is the function with the height in feet from the ground as the independent variable? After about how many seconds were the keys 4 feet above the ground?
+259 f(x)=-16x^2+32
x=time in sec.
y=heigh in feet
After about how many seconds were the keys 4 feet above the ground?
So when is f(x)=4
-16x^2+32=4
solve it and u get the result:
\(x= -sqrt(7)/2 , x= sqrt(7)/2\)
Only the positive result is the right answer, as theres no negative time.
Oh forget the first part:
When u want to have the heigh as x you need to rotate the graph by 90 against the clock.
Im not sure how to do this though.
When u rotate the graph every coordiante of x/y becomes y/-x. Example: 1/3 becomes 3/-1
That means in the equation every x becomes y and every y becomes -x.
-16x^2+32=f(x)
y is equal to f(x)
-16y^2+32=-x. I *-1
16y^2-32=x. I +32
16y^2= x+32. I/16
y^2. = x/16 + 2. I sqrt
\(y = \sqrt[2]{\frac{x}{16}} + \sqrt[2]{2}\)
\(f(x) = \sqrt[2]{\frac{x}{16}} + \sqrt[2]{2}\)
Im not sure if this answer is right.
+259 f(x)=-16x^2+32
x=time in sec.
y=heigh in feet
After about how many seconds were the keys 4 feet above the ground?
So when is f(x)=4
-16x^2+32=4
solve it and u get the result:
\(x= -sqrt(7)/2 , x= sqrt(7)/2\)
Only the positive result is the right answer, as theres no negative time.
Oh forget the first part:
When u want to have the heigh as x you need to rotate the graph by 90 against the clock.
Im not sure how to do this though.
When u rotate the graph every coordiante of x/y becomes y/-x. Example: 1/3 becomes 3/-1
That means in the equation every x becomes y and every y becomes -x.
-16x^2+32=f(x)
y is equal to f(x)
-16y^2+32=-x. I *-1
16y^2-32=x. I +32
16y^2= x+32. I/16
y^2. = x/16 + 2. I sqrt
\(y = \sqrt[2]{\frac{x}{16}} + \sqrt[2]{2}\)
\(f(x) = \sqrt[2]{\frac{x}{16}} + \sqrt[2]{2}\)
Im not sure if this answer is right.
+129852 What is the function with the height in feet from the ground as the independent variable?
let f(x) = h
h = −16x^2 + 32
h − 32 = −16x^2 divide by −16
[ h − 32] / − 16 = x^2
[32 − h ] / 16 = x^2 take the positive root of both sides
√[32 − h ] / 4 = x
After about how many seconds were the keys 4 feet above the ground ?
√[32 − 4 ] / 4 = √[28 ] / 4 = √[7 ] / 2 sec ≈ 1.32 sec
