Question

Here are two steps from the derivation of the quadratic formula.

Answer 1

ANSWER

C. Factoring a perfect square trinomial.

EXPLANATION

The first step shown is:

${x}^{2} + \frac{b}{a}x + ( \frac{b}{2a} )^{2} = - \frac{c}{a} + ( \frac{b}{2a} )^{2}$

Observe that the left hand side is a perfect square trinomial.

In other words, the left hand side is of the form,

${m}^{2} + 2mn + {n}^{2}$

which can be factored as:

${m}^{2} + 2mn + {n}^{2} = {(m + n)}^{2}$

When we factor the perfect square trinomial on the left hand side, we obtain:

$( x + \frac{b}{2a} )^{2} = - \frac{c}{a} + ( \frac{b}{2a} )^{2}$

The correct answer is C