Final answer:
To determine the equation for a graph that has undergone a vertical compression by a factor of four, multiply the original function f(x)=x² by 0.25. The resulting equation is f(x)=0.25x².
Step-by-step explanation:
To determine the equation for the graph of f(x)= x² that has been compressed by a factor of four, we must modify the original function to reflect this transformation. A vertical compression of a function by a factor of k < (1) involves multiplying the function by k. Therefore, since we are compressing by a factor of four, we multiply the original function by ⅔ (or 0.25), the reciprocal of the compression factor.
The new equation will be:
f(x) = ⅔x²
In expanded form, this is:
f(x) = 0.25x²
This new function will graphically appear to be squished along the y-axis when compared to the original f(x) = x² graph.