Question

The first step for deriving the quadratic formula from the quadratic equation, 0 = ax2 bx c, is shown.step 1: –c = ax2 bxwhich best explains or justifies step 1?a.subtraction property of equalityb.completing the squarec.factoring out the constantd.zero property of multiplication

Answer 1

Answer:

option (b) is correct.

First step to solve for deriving the quadratic formula from the quadratic equation is completing the square.

Step-by-step explanation:

Given : the quadratic equation $ax^2+bx+c=0$

We have to find the first step for deriving the quadratic formula from the quadratic equation.

Quadratic formula  is given by $\frac{-b\pm\sqrt{b^2-4ac}}{2a}$

Consider the given quadratic equation $ax^2+bx+c=0$

Divide the equation by a, we get,

$x^2+\frac{b}{a}x+\frac{c}{a}=0$

Take $\frac{c}{a}$ to other side, we get,

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

Add $(\frac{b}{2a})^2$ to both side, we get,

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

Thus, the left side is in the form of $(a+b)^2=a^2+b^2+2ab$

On solving, we get,

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

Then solve for x , we get quadratic formula $\frac{-b\pm\sqrt{b^2-4ac}}{2a}$

Thus, first step to solve for deriving the quadratic formula from the quadratic equation is completing the square.

Thus, option (b) is correct.

Answer 2

In deriving the quadratic formula from the equation 0=ax^2+bx+c where the first step is -c=ax^2+bx, subtraction property of equality best justifies step one. It states that when you subtract the same number in both sides of the equation, the expressions on both sides remain equal. In this case, we subtracted c from both sides resulting to the equation -c=ax^2+bx.