SAT Math · Study & Practice

Quadratic Equations

Quadratic equations are a cornerstone of SAT Advanced Math. This chapter covers the standard form, solving by factoring, the square-root method, completing the square and the quadratic formula. Read each topic, try the problems with the hint ladder, then take the 8-question topic test.

Topics

1 Standard Form 4 worked · 5 practice · 8-Q test Start → 2 Factoring Method 4 worked · 5 practice · 8-Q test Start → 3 Square Root Method 4 worked · 5 practice · 8-Q test Start → 4 Completing the Square 4 worked · 5 practice · 8-Q test Start → 5 Quadratic Formula 4 worked · 5 practice · 8-Q test Start →

Chapter test

📝 Quadratic Equations — Chapter Test

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Formula Reference Sheet

This chapter

Forms & solving

Standard form	ax² + bx + c = 0
Zero-product rule	if AB = 0 then A = 0 or B = 0
Square-root method	x² = k ⇒ x = ±√k
Quadratic formula	x = (−b ± √(b² − 4ac)) / 2a

Discriminant

Discriminant	D = b² − 4ac
Two real roots	D > 0
One real root	D = 0
No real roots	D < 0

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Area & Circumference

Circle area	A = πr²
Circle circumference	C = 2πr
Rectangle	A = ℓw
Triangle	A = ½ b h

Volume

Rectangular box	V = ℓwh
Cylinder	V = πr²h
Sphere	V = 4⁄3 πr³
Cone	V = 1⁄3 πr²h
Pyramid	V = 1⁄3 ℓwh

Right triangles

Pythagorean theorem	a² + b² = c²
30°–60°–90°	sides x : x√3 : 2x
45°–45°–90°	sides s : s : s√2

Constants

Degrees in a circle	360°
Radians in a circle	2π
Angles of a triangle	sum = 180°