If the graph of the function h defined by h(x)=5x^2-4 is translated vertically downward by 3 units, it becomes the graph of a function g. find the expression for g(x)

 
g(x) = h(x) – 3

Explanation: 
To translate a function by shifting it up or down, you are moving it along the y-axis. This means that you have to alter the y-value when you are shifting it, so if h(x) is the y-value then to move it down 3 units you are subtracting 3 from whatever h(x) equals: 
h(x) – 3 = g(x) 

To check this out, say x is 5 in h(x):
h(5) = 5 – 4 
h(5) = 5(25) – 4
h(5) = 125 – 4 
h(5) = 121 
So (5, 121) 
If you shift this down three units it should be (5, 118) 
Try 5 in g(x): 
g(5) = h(5) – 3 
g(5) = 121 – 3 
g(5) = 118 
So (5, 118) 
Yes.