SOLUTION: For the function h(x)=-(x-5)^2+3, do the following: (a)Identify the parent function (b)Describe the transformation from f to h (c)Sketch the graph of h(x)

Algebra ->  Functions -> SOLUTION: For the function h(x)=-(x-5)^2+3, do the following: (a)Identify the parent function (b)Describe the transformation from f to h (c)Sketch the graph of h(x)      Log On


   

Question 885670: For the function h(x)=-(x-5)^2+3, do the following:
(a)Identify the parent function
(b)Describe the transformation from f to h
(c)Sketch the graph of h(x)
Answer by Edwin McCravy(20056) About Me  (Show Source):
You can put this solution on YOUR website!
%22h%28x%29%22%22%22=%22%22-%28x-5%29%5E2%2B3

The parent function is the red graph below.

%22f%28x%29%22%22%22=%22%22x%5E2

Then we will multiply the right side by -1, getting

%22k%28x%29%22%22%22=%22%22-x%5E2

which will reflect it across or into the x-axis, the green
graph below.  

Then we will replace x in the the right side by x-5, getting

%22g%28x%29%22%22%22=%22%22-%28x-5%29%5E2

which will shift it 5 units to the right, the light blue (aqua) 
graph below.

Finally we will add +3 to the the right side, getting

%22h%28x%29%22%22%22=%22%22-%28x-5%29%5E2%2B3

which will shift it 3 units upward, the purple graph below.
 


Edwin