Question

The first few steps in deriving the quadratic formula are shown.

Answer 1

The distributive property needs to be applied to determine the value to add to the left side of the equation to balance the sides of the equation

Deriving the Quadratic Formula

From the question, we are to determine the statement that best explain why $\frac{b^{2} }{4a^{2} }$ is not added to the left side of the equation in the last step shown

The last step shown in the table is

$-c + \frac{b^{2} }{4a } = a(x^{2} + \frac{b}{a} x + \frac{b^{2} }{4a^{2} })$

From the first few steps, we have

$-c = ax^{2} + bx$

By factoring the right side

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

Now, we want to add  $\frac{b^{2} }{4a^{2} }$ to both sides of the equation

As shown in the last step, we have the term $\frac{b^{2} }{4a^{2} }$ in the parenthesis.

If we apply the distributive property,

$-c + \frac{b^{2} }{4a } = a(x^{2} + \frac{b}{a} x + \frac{b^{2} }{4a^{2} })$

We get

$-c + \frac{b^{2} }{4a } = ax^{2} + bx + \frac{b^{2} }{4a }$

This means, the term that was actually added to the right side was $\frac{b^{2} }{4a }$

Hence,

The distributive property needs to be applied to determine the value to add to the left side of the equation to balance the sides of the equation

Learn more on The Quadratic formula here: brainly.com/question/9764778

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