Question

The function y=x^2-4x+8 approximates the height,y, of a bird, and its horizontal distance,x, as it flies from one fence post to another. All distances are in feet.Complete the square to find and interpret the extreme value (vertex). Select two answers: one extreme value and one interpretation

Answer 1

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.

Extreme value: Therefore, extreme value ( minimum value) of the function is 12.

With respect to problem, we can interprit it as

Interpretation: The lowest height of the bird can fly is 12 feet.