When should I use the quadratic formula instead of factoring?

Use factoring when integer factors are obvious; use the formula whenever they are not, since it always works.

Quadratic Equation Formulas — Examples and Uses

Everything needed to solve and analyse a quadratic, in one place.

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

Solves ax² + bx + c = 0 for any real coefficients with a ≠ 0.

$\Delta = b^2 - 4ac$

Positive: two real roots. Zero: one repeated root. Negative: two complex roots.

$x = -\frac{b}{2a}$

The axis of symmetry and the x-coordinate of the turning point.

$a(x - r_1)(x - r_2)$

Useful when the roots are known or the quadratic factors over the integers.

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Enter a problem that uses one of these formulas and follow the worked steps.

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When should I use the quadratic formula instead of factoring?: Use factoring when integer factors are obvious; use the formula whenever they are not, since it always works.