Quadratic Equations • Topic 1 of 5

Standard Form

The standard form of a quadratic equation is ax² + bx + c = 0, where a ≠ 0. Putting an equation into this form — by moving every term to one side so the other side is 0 — is the first step before factoring or using the quadratic formula. Here a is the leading coefficient, b the linear coefficient and c the constant. Identifying a, b and c correctly (with their signs) is essential, because the quadratic formula and the discriminant both depend on them. The SAT frequently gives a quadratic in a rearranged form and expects you to standardise it first.

✅ Solved examples

1. Write x² + 3x = 10 in standard form.
Move 10 to the left: x² + 3x − 10 = 0.
2. Identify a, b, c in 2x² − 5x + 3 = 0.
a = 2, b = −5, c = 3.
3. Write 4x = x² − 5 in standard form.
Bring all terms to one side: x² − 4x − 5 = 0.
4. Identify c in x² − 9 = 0.
There is no x-term (b = 0); the constant is c = −9.

✏️ Practice — try these, take hints as needed

1. Write x² + 2x = 8 in standard form.
Move 8 to the left.
Set equal to 0.
—
x² + 2x − 8 = 0.
2. Identify a, b, c in 3x² + 4x − 1 = 0.
Match ax² + bx + c.
Read coefficients with signs.
—
a = 3, b = 4, c = −1.
3. Write 6x = x² + 5 in standard form.
Move all terms to one side.
x² − 6x + 5 = 0.
—
x² − 6x + 5 = 0.
4. Identify b in x² − 7x = 0.
Match the linear coefficient.
No constant term.
—
b = −7.
5. Write 2x² = 8x − 6 in standard form.
Move all to one side.
2x² − 8x + 6 = 0.
—
2x² − 8x + 6 = 0.

📝 Topic test — 8 questions

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