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.

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

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

$Δ = b^{2} - 4 a c$

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

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

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.