Question

F(x)=x^2-8x+44 in vertex form

Answer 1

`f(x)=(x-4)^2+28`

Explanation:

Here are the steps to convert the quadratic function
`f(x)=x^2-8x+44` into vertex form:

Step 1: Group the
`x` terms together:

`f(x)=(x^2-8x)+44`

Step 2: Complete the square within the parentheses by adding and subtracting the square of half the coefficient of the
`x` term:

`f(x)=(x^2-8x+16)-16+44`

Step 3: Rearrange the expression:

`f(x)=(x^2-8x+16)-16+44`

Step 4: Factor the perfect square trinomial
`(x^2-8x+16)`:

`f(x)=(x-4)^2-16+44`

Step 5: Simplify and combine constants:

`f(x)=(x-4)^2+28`

Therefore, the quadratic function
`f(x)=x^2-8x+44` in vertex form is
`f(x)=(x-4)^2+28.` The vertex of the parabola is located at the point
`(4,28)`.