Question

Express 2x² — 12x + 23 in the form a (x + b)² + c.
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Answer 1

Below

Explanation:

This is changing the form of the parabola from quadrtatic form to vertex form using the 'complete the square method'

2x^2 - 12x + 23 first, to complete the square the x^2 coefficient must be =1

so factor out 2 form the x components

2 (x^2 -6x) + 23 now....take 1/2 of the 'x' coefficient ( this would be -3)

square it and add this value in the parentheses and subtract it on the outside of the parentheses ( it will be multiplied by the '2' when you need to subtract it....making it -18) )

2 (x^2 - 6x +9 ) - 18 + 23 now reduce the underlined portion

2(x-3)^2 +5 Done .