Question

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

What took place between the first step and the second step?
*Apex

Answer 1

FACTORING A PERFECT SQUARE TRINOMIAL!

Explanation:

GOT IT CORRECT ON 3.8.3 AP-EX...

it's not sq root because that comes afterwards.

it's not completing the square because that's

x^2+ bx/a +(b/2a)^2=-c/a+(b/2a)^2

Then from there it's

x^2 + bx/a + b^2/4a^2 = -c/a + b^2/4a^2

(x + b/2a)^2 = b^2/4a^2 -c/a

Then that step ends. If you don't believe me look at study 3.3.1 page 13.

This will help!

Answer 2

C. Factoring a perfect square trinomial.

EXPLANATION

The first step shown is:

`{x}^(2) + (b)/(a)x + ( (b)/(2a) )^(2) = - (c)/(a) + ( (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 + (b)/(2a) )^(2) = - (c)/(a) + ( (b)/(2a) )^(2)`

The correct answer is C