SOLUTION: Determine the vertex (h,k) of {{{f(x)= (x-4)^2-1}}} I am supposed to find the x intercept(s), y intercept(s) and graph the function. Thank you in advance for your help.

Algebra ->  Finite-and-infinite-sets -> SOLUTION: Determine the vertex (h,k) of {{{f(x)= (x-4)^2-1}}} I am supposed to find the x intercept(s), y intercept(s) and graph the function. Thank you in advance for your help.      Log On


   

Question 196165: Determine the vertex (h,k) of f%28x%29=+%28x-4%29%5E2-1
I am supposed to find the x intercept(s), y intercept(s) and graph the function.
Thank you in advance for your help.
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Any value I pick for x except x+=+4
will give me a value for f%28x%29 which is
greater than -1 by some amount, so
(4, -1) is a minimum vertex.
The x-intercept is where f%28x%29=0
f%28x%29=+%28x-4%29%5E2-1
0+=+%28x-4%29%5E2+-+1
x=5
x=3
The x-intercepts are (5,0) and (3,0)
The y-intercept is where x=0
f%28x%29=+%28x-4%29%5E2-1
f%28x%29=+%280-4%29%5E2-1
f%28x%29=+15
The y-intercept is at (0,15)
Here's the plot:
+graph%28+500%2C+500%2C+-2%2C+10%2C+-2%2C+20%2C+%28x-4%29%5E2+-+1%29+