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Free Algebra I Quadratic Functions & Equations Worksheets

349+ Texas TEKS-aligned practice questions on quadratic functions & equations. Print at home or practice online with a built-in AI tutor. No sign-up. No paywall.

Looking for quadratic functions & equations worksheets for Algebra I? This page has 349+ TEKS-aligned practice questions on this exact topic. Every question goes through an AI quality gate before publishing — no typos, no wrong answer keys, no factually-broken explanations.

Below: a sample of 8 questions with answers and explanations so you can see what's on the worksheet before you print. Each question has the correct choice marked and a one-line "why" so kids who get it wrong understand the fix.

Solve by factoring: x² + 0x − 64 = 0

  1. x = -7, x = 9
  2. x = -8, x = 8
  3. x = 8, x = -8
  4. x = -9, x = 7

Why: Factors as (x + -8)(x + 8) = 0, so x = 8 or x = -8.

Solve by factoring: x² + 7x + 6 = 0

  1. x = -5, x = 0
  2. x = 6, x = 1
  3. x = -6, x = -1
  4. x = -7, x = -2

Why: Factors as (x + 1)(x + 6) = 0, so x = -1 or x = -6.

Solve by factoring: x² + 2x − 63 = 0

  1. x = -8, x = 8
  2. x = 9, x = -7
  3. x = -9, x = 7
  4. x = -10, x = 6

Why: Factors as (x + -7)(x + 9) = 0, so x = 7 or x = -9.

Solve by factoring: x² − 6x − 27 = 0

  1. x = -2, x = 10
  2. x = -4, x = 8
  3. x = 3, x = -9
  4. x = -3, x = 9

Why: Factors as (x + 3)(x + -9) = 0, so x = -3 or x = 9.

Use the quadratic formula to solve: 3x² + 6x − 24 = 0

  1. x = -3, x = 3
  2. x = -5, x = 1
  3. x = 4, x = -2
  4. x = -4, x = 2

Why: x = (−b ± √(b² − 4ac)) / (2a). Discriminant = 324, √324 = 18. Roots: -4, 2.

Use the quadratic formula to solve: 3x² + 0x − 3 = 0

  1. x = -2, x = 0
  2. x = 1, x = -1
  3. x = 0, x = 2
  4. x = -1, x = 1

Why: x = (−b ± √(b² − 4ac)) / (2a). Discriminant = 36, √36 = 6. Roots: -1, 1.

Use the quadratic formula to solve: 3x² + 0x − 48 = 0

  1. x = 4, x = -4
  2. x = -3, x = 5
  3. x = -4, x = 4
  4. x = -5, x = 3

Why: x = (−b ± √(b² − 4ac)) / (2a). Discriminant = 576, √576 = 24. Roots: -4, 4.

Use the quadratic formula to solve: 3x² − 9x − 54 = 0

  1. x = 3, x = -6
  2. x = -3, x = 6
  3. x = -2, x = 7
  4. x = -4, x = 5

Why: x = (−b ± √(b² − 4ac)) / (2a). Discriminant = 729, √729 = 27. Roots: -3, 6.

Common questions

Are these worksheets really free?

Yes. Free to print, free to practice online. No email, no sign-up, no paywall. We make money from optional paid features (toy redemption with real cents), not from the worksheets.

What TEKS standards does this cover?

This unit aligns to multiple Algebra I math TEKS standards.

How many total questions are available?

349+ questions in our Algebra I Quadratic Functions & Equations bank. Print as many 20-question worksheets as you like — each one pulls a fresh set so your kid doesn't see the same questions twice.

Where do these questions come from?

Generated by our AI pipeline, then quality-gated by two independent models (gpt-4o for content review, Claude Sonnet 4.5 for math verification) before publishing. Every question is tagged to a specific TEKS standard and modeled on real STAAR item shapes.