SAT Math · Study & Practice

Quadratic Functions

Quadratic functions describe parabolas — the U-shaped graphs the SAT tests through vertices, intercepts and transformations. This chapter covers parabolas, vertex form, the axis of symmetry, maximum and minimum values and graph interpretation. Read each topic, try the problems with the hint ladder, then take the 8-question topic test.

Topics

1 Parabolas 4 worked · 5 practice · 8-Q test Start → 2 Vertex Form 4 worked · 5 practice · 8-Q test Start → 3 Axis of Symmetry 4 worked · 5 practice · 8-Q test Start → 4 Maximum and Minimum Values 4 worked · 5 practice · 8-Q test Start → 5 Graph Interpretation 4 worked · 5 practice · 8-Q test Start →

Chapter test

📝 Quadratic Functions — Chapter Test

25 fresh questions · timed · full solutions

Start chapter test →

📊 My SAT analytics

Track scores, accuracy by topic and progress over time.

View analytics →

Formula Reference Sheet

This chapter

Parabola basics

Standard form	y = ax² + bx + c
Opens up / down	a > 0 up, a < 0 down
Axis of symmetry	x = −b/(2a)
y-intercept	(0, c)

Vertex

Vertex form	y = a(x − h)² + k, vertex (h, k)
Vertex x	x = −b/(2a)
Min / max value	the k-value (min if a>0, max if a<0)

Digital SAT reference

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°