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 $a$? $\bigcirc$ $a = \frac{b}{2x}$ $\bigcirc$ $a = \frac{-b}{2x}$ $\bigcirc$ $a = \frac{1}{2}bx$

Explanation:

Step1: Start with the given formula

We have the formula for the axis of symmetry: \( x = \frac{-b}{2a} \). Our goal is to solve for \( a \).

Step2: Cross - multiply to eliminate the fraction

Multiply both sides of the equation by \( 2a \) to get rid of the denominator on the right - hand side. This gives us \( x\times(2a)=\frac{-b}{2a}\times(2a) \), which simplifies to \( 2ax=-b \).

Step3: Solve for \( a \)

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

Answer:

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