We are given function y=x^2-4x+8.
We need to convert it in vertex form by completing the square.
In order to apply completeing the square, first we need to make first two terms in Parenthesis.
y = (x^2 -4x ) +8.
Now, we need to check the coefficent of x there.
The coefficent of x is -4.
Now, divide -4 by 2, we get -2.
Now, we need to find the square of -2.
We get (-2)^2 = 4.
Adding 4 inside Parenthesis and subtract outside Parenthesis from 8.
y = (x^2 -4x +4 ) +8 +4.
Now, we need to find the perfect square of Parenthesis (x^2 -4x +4 ).
(x^2 -4x +4 ) = (x-2)^2.
Replacing (x-2)^2 for (x^2 -4x +4) , we get
y = (x-2)^2 +8 +4.
Now adding 8 and 4, we get
y = (x-2)^2 +12.
That is the final vertex form.
On comaring with vertex form y=a(x-h)^2+h, we got vertex (h,k) = (2,12).
y-coordinate of the vertex represents extreme value.
<u>Extreme value:</u> Therefore, extreme value ( minimum value) of the function is 12.
With respect to problem, we can interprit it as
<u>Interpretation:</u> The lowest height of the bird can fly is 12 feet.
