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Learning Focus

Choose an efficient method for solving a quadratic equation.

Big idea

• Square roots: form $ax^2+c=0$ (no $x$ term).
• Factoring: when integers multiply to $ac$ and add to $b$ easily.
• Completing the square: when $a=1$ and $b$ is even.
• Quadratic formula: always works:

$x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}.$

Worked example

$3x^2-12=0$: $x^2=4$, so $x=\pm2$. Square roots is fastest.

Takeaways

• Look at the structure before choosing a method.
• Check for a missing $b$ or $c$ term.
• The quadratic formula is the reliable fallback.