SOLUTION: I'm not even sure if this is where I put this answer. I have graphed and done equations, how do I figure this out? Is it a matter of doing equation on graphing calculator and the d

Algebra ->  Rational-functions -> SOLUTION: I'm not even sure if this is where I put this answer. I have graphed and done equations, how do I figure this out? Is it a matter of doing equation on graphing calculator and the d      Log On


   

Question 280229: I'm not even sure if this is where I put this answer. I have graphed and done equations, how do I figure this out? Is it a matter of doing equation on graphing calculator and the difference?



Describe the transformations from f(x) = x2 to the function f(x) = -4 – 3x2.
shift up 4 units and 3 units to the left
shift down 4 units and 3 units to the right
shift down 4 units, reflect about the x-axis, vertical stretch of 3
shift up 4 units, reflect about the x-axis, horizontal stretch of 3
Thanks for anyone who helps!
Answer by jsmallt9(3758) About Me  (Show Source):
You can put this solution on YOUR website!
f%28x%29+=+x%5E2
To avoid confusion I'm going to use a different name for the second function:
g%28x%29+=+-4+-+3x%5E2
Now I'll rewrite g(x) in a form which we can use to find the answer:
g%28x%29+=+%28-1%29%283%29x%5E2+%2B+%28-4%29
Since f%28x%29+=+x%5E2, this becomes:
g%28x%29+=+%28-1%29%283%29%28f%28x%29%29+%2B+%28-4%29
Looking at g(x) in this way we can see what transformations are being applied to f(x) to turn it into g(x):
  • The multiplication of f(x) by 3 means a vertical stretch by a factor of 3.
  • The multiplication of f(x) by -1 means a vertical "flip" (i.e. a reflection in the x-axis)
  • The addition of -4 means a downward shift of 4 units.