Question

Express x²-5x+8 in the form (x-a)²+b where a and b are top heavy fractions. Does anyone know how to answer this?

Answer 1

`x^2 - 5x + 8` can be expressed as
`(x - 5/4)^2 + 1.75`. This form satisfies the requirements of the question, where a (5/4) and b (1.75) are both top-heavy fractions.

Isolate the quadratic term:

Start by moving the constant term to the right side of the equation:
`x^2 - 5x = -8`.

Half the coefficient of the linear term:

Divide the coefficient of the linear term (which is -5) by 2 and square it. In this case, -5/2 squared is 25/4.

Add and subtract the squared term inside the parentheses:

Add and subtract the squared term inside the parentheses. This won't change the overall value of the expression, but it will allow us to group terms into a perfect square.

`x^2 - 5x + 25/4 - 25/4 = -8 + 25/4`

Rewrite as a squared term:

Group the terms inside the parentheses and factor out a 4:

`4(x^2 - 5x/4 + 6.25/16)`

Recognize the perfect square:

The expression inside the parentheses is now a perfect square trinomial:
`(x - 5/4)^2`

Combine constant terms:

Add the constant term from step 3 outside the parentheses to complete the expression:

`(x - 5/4)^2 + 1.75`