When should I use the quadratic formula instead of factoring?

Whenever factoring isn't quick — the formula works on every quadratic. If the discriminant isn't a perfect square, the equation didn't factor nicely anyway.

What does the discriminant tell you?

b² − 4ac predicts the solutions before you solve: positive means two real solutions, zero means one repeated solution, negative means no real solutions.

Yes — this skill is one of the free ones. Every unit opens with free skills, no account needed. Premium ($6/month or $30/year) unlocks every skill plus the parent progress dashboard.

How is this different from IXL?

No punishing score. A wrong answer gives you a step-by-step explanation, not a number that drops — and every question is reviewed by a human before you see it.

Algebra 2 practice

The Quadratic Formula — Practice

Solve any quadratic with $x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}$ — free, no account, with every step explained.

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What you'll practice

The quadratic formula solves every equation of the form $ax^2 + bx + c = 0$ , including the ones factoring can't touch. These questions cover identifying $a$ , $b$ , $c$ (signs included), simplifying the discriminant $b^2 - 4ac$ , and using the discriminant to predict how many real solutions exist before solving.

Worked example

Solve $x^2 - 4x - 5 = 0$ .

Identify $a = 1$ , $b = -4$ , $c = -5$ .
Discriminant: $b^2 - 4ac = (-4)^2 - 4(1)(-5) = 16 + 20 = 36$ .
$x = \frac{-(-4) \pm \sqrt{36}}{2(1)} = \frac{4 \pm 6}{2}$ .
$x = \frac{10}{2} = 5$ or $x = \frac{-2}{2} = -1$ . Check: $25 - 20 - 5 = 0$ . ✓

Common mistakes

Dropping the sign of $b$ : for $b = -4$ , the formula's $-b$ is $+4$ . Write the substitution in parentheses before simplifying.
Discriminant sign error: $-4ac$ with a negative $c$ becomes positive — $16 + 20$ , not $16 - 20$ .
Dividing only one term by $2a$ : BOTH the $-b$ and the $\pm\sqrt{\ }$ part sit over $2a$ .

Try a few

1. Solve $x^2 + 2x - 8 = 0$ .

$x = 2$ or $x = -4$
$x = -2$ or $x = 4$
$x = 1$ or $x = -8$
$x = 2$ or $x = 4$

2. Solve $2x^2 - 3x - 2 = 0$ .

$x = 2$ or $x = -\frac{1}{2}$
$x = -2$ or $x = \frac{1}{2}$
$x = 1$ or $x = -2$
$x = 2$ or $x = \frac{1}{2}$

3. What does the discriminant of $x^2 - 6x + 9 = 0$ tell you?

$b^2-4ac = 0$ : exactly one repeated real solution
$b^2-4ac > 0$ : two distinct real solutions
$b^2-4ac < 0$ : no real solutions
The discriminant can't be found without solving

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FAQ

When should I use the quadratic formula instead of factoring?: Whenever factoring isn't quick — the formula works on every quadratic. If the discriminant isn't a perfect square, the equation didn't factor nicely anyway.
What does the discriminant tell you?: b² − 4ac predicts the solutions before you solve: positive means two real solutions, zero means one repeated solution, negative means no real solutions.
Is Cramzoo free?: Yes — this skill is one of the free ones. Every unit opens with free skills, no account needed. Premium ($6/month or $30/year) unlocks every skill plus the parent progress dashboard.
How is this different from IXL?: No punishing score. A wrong answer gives you a step-by-step explanation, not a number that drops — and every question is reviewed by a human before you see it.

Related Algebra 2 skills

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No login, no card. Open Algebra 2 and pick the tile.