Question

the axis of symmetry for a quadratic equation can be found using the formula $x = \frac{-b}{2a}$, where $a$ and $b$ are coefficients in the quadratic equation and $x$ represents the values along a vertical line on the coordinate plane. what is the equation when solved for $a$?\
\\(\bigcirc\\) $a = \frac{b}{2x}$\
\\(\bigcirc\\) $a = \frac{-b}{2x}$\
\\(\bigcirc\\) $a = \frac{1}{2}bx$\
\\(\bigcirc\\) $a = -\frac{1}{2}bx$

Explanation:

Step1: Start with the given formula

We have the formula for the axis of symmetry: \( x = \frac{-b}{2a} \)

Step2: Cross - multiply to eliminate the fraction

Multiply both sides of the equation by \( 2a \) to get \( 2a\times x=\frac{-b}{2a}\times2a \). The right - hand side simplifies to \( -b \), so we have \( 2ax=-b \)

Step3: Solve for \( a \)

Divide both sides of the equation \( 2ax = - b \) by \( 2x \) (assuming \( x
eq0 \)). So \( a=\frac{-b}{2x} \)

Answer:

B. \( a=\frac{-b}{2x} \)