# Axis of Symmetry $x=-\dfrac{b}{2a}$

The equation of the axis of symmetry of $y=ax^2+bx+c$ is $x=-\dfrac{b}{2a}$.

### Example 1

Find the equation of the axis of symmetry of $y=x^2+4x-2$.

\begin{align} \displaystyle x &= -\dfrac{b}{2a} \\ &= -\dfrac{4}{2 \times 1} \\ \therefore x &= -2 \\ \end{align}

### Example 2

Find the equation of the axis of symmetry of $y=-2x^2-12x+3$.

\begin{align} \displaystyle x &= -\dfrac{b}{2a} \\ &= -\dfrac{-12}{2 \times (-2)} \\ \therefore x &= -3 \\ \end{align}

### Example 3

The equation of the axis of symmetry of $y=ax^2-(a+4)x-3$ is $x=1$. Find $a$.

\begin{align} \displaystyle -\dfrac{b}{2a} &= 1 \\ -\dfrac{-(a+4)}{2 \times a} &= 1 \\ \dfrac{a+4}{2a} &= 1 \\ a+4 &= 2a \\ \therefore a &= 4 \\ \end{align}