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

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.

answer

explanation

the area of a circle is calculated using the formula

or

we can use any of the above formulae to calculate the required. preferably, let us use the latter since the diameter is

we substitute the diameter into the formula to get:

this is the exact value for the area of the circle.

the correct answer is a

the number of possible outcomes that do not show a 1 on the first spinner and show the number 4 on the second spinner is 2.

spinner 1 spinner 2

1                     1

1                     2

1                     3

1                     4

2                   1

2                   2

2                   3

2                   4   = not 1, and 4

3                   1

3                   2

3                   3

3                   4 = not 1, and 4

only 2 outcomes have passed the given condition.

step-by-step explanation: