Question

Some of the steps in the derivation of the quadratic formula are shown.

Step 3: –c + StartFraction b squared Over 4 a EndFraction = a(x squared + StartFraction b Over a EndFraction x + StartFraction b squared Over 4 a squared EndFraction)

Step 4a: –c + StartFraction b squared Over 4 a EndFraction = a(x + StartFraction b Over 2 a EndFraction) squared

Step 4b: negative StartFraction 4 a c Over 4 a EndFraction + StartFraction b squared Over 4 a EndFraction = a(x + StartFraction b Over 2 a EndFraction) squared

Which best explains or justifies Step 4b?

factoring a polynomial
multiplication property of equality
converting to a common denominator
addition property of equality

Answer 1

Converting to a common denominator.

They rewrote −c as −4ac/(4a) so it can be combined with b^2/(4a), giving (b^2 − 4ac)/(4a) on the left.