Answered

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The axis of symmetry for a quadratic equation can be found using the formula [tex]$x=\frac{-b}{2a}[tex]$[/tex], where [tex]$[/tex]a[tex]$[/tex] and [tex]$[/tex]b[tex]$[/tex] are coefficients in the quadratic equation and [tex]$[/tex]x$[/tex] represents the values along a vertical line on the coordinate plane.

What is the equation when solved for [tex]$a$[/tex]?

A. [tex]$a=\frac{b}{2x}$[/tex]

B. [tex]$a=\frac{-b}{2x}$[/tex]

C. [tex]$a=\frac{1}{2}bx$[/tex]

D. [tex]$a=-\frac{1}{2}bx$[/tex]

Sagot :

GinnyAnswer
To solve the formula \( x = \frac{-b}{2a} \) for \( a \), we need to isolate \( a \) on one side of the equation. Let us proceed step-by-step:

1. Start with the given formula:
[tex]\[ x = \frac{-b}{2a} \][/tex]

2. Multiply both sides of the equation by \( 2a \) to get rid of the denominator on the right-hand side:
[tex]\[ 2a \cdot x = -b \][/tex]

3. Simplify the equation:
[tex]\[ 2ax = -b \][/tex]

4. To isolate \( a \), divide both sides of the equation by \( 2x \):
[tex]\[ a = \frac{-b}{2x} \][/tex]

Thus, when the formula \( x = \frac{-b}{2a} \) is solved for \( a \), the equation is:

[tex]\[ a = \frac{-b}{2x} \][/tex]

So the correct answer is:
[tex]\[ a = \frac{-b}{2x} \][/tex]
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