The force in newtons needed to stretch a certain spring x centimeters from its resting position is given by the function f(x)=8x^2 where 8 is the spring constant. Find the force needed to stretch the spring 4 centimeters.
f(4)=8(4)^2
This looks more like late middle school math to me. Anyway, the equation is f(4) = 8(4^2) = 8(16) = 128. Notice I replaced x with 4 to set up the equation, so that it reads "f of 4 (the force needed to stretch 4 centimeters) equals 8 times 4 to the power of two"
I don't know of any springs for which the restoring force is proportional to the square of the displacement.
It is apparently not unusual for the word "college" to proceed a subject that should have been learned in high school or earlier.
To find the force needed to stretch the spring 4 centimeters, we need to substitute the value x = 4 into the function f(x) = 8x^2:
f(4) = 8 * (4)^2
First, we square 4:
f(4) = 8 * 16
Next, multiply 8 by 16:
f(4) = 128
Therefore, the force needed to stretch the spring 4 centimeters is 128 Newtons.