# Axis of Symmetry of Quadratic Graphs

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}
{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 2, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 1.0000100135803223, "perplexity": 1233.4927792393837}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.3, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2023-14/segments/1679296943746.73/warc/CC-MAIN-20230321193811-20230321223811-00176.warc.gz"}