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 $a$.

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





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