SOLUTION: Consider the function: f(x)=(x-2)^2-4 Find the coordinates of the vertex, (x,y) Make sure to show all work

Algebra ->  Functions -> SOLUTION: Consider the function: f(x)=(x-2)^2-4 Find the coordinates of the vertex, (x,y) Make sure to show all work      Log On


   

Question 1053781: Consider the function: f(x)=(x-2)^2-4
Find the coordinates of the vertex, (x,y)
Make sure to show all work
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
If this 2nd degree equation has 2 real roots,
then the vertex will be exactly midway between
the roots
+f%28x%29+=+%28+x-2+%29%5E2+-+4+
Find the roots ( if they exist ) by making +f%28x%29+=+0+
+%28+x+-+2+%29%5E2+-+4+=+0+
I can see by looking at this that
+x+=+0+ and
+x+=+4+
are the roots
+%28+0+%2B+4+%29+%2F+2+=+2+
-----------------------
So, +x+=+2+ is the x-value of the vertex
Plug this value back into the equation
+f%282%29+=+%28+2+-+2+%29%5E2+-+4+
+f%282%29+=+0+-+4+
+f%282%29+=+-4+
-------------------
So, the vertex is at ( 2, -4 )
---------------------------
Here's a plot of the equation:
+graph%28+400%2C+400%2C+-10%2C+10%2C+-10%2C+10%2C+%28+x+-+2+%29%5E2+-+4+%29+
My answer looks right