Completing the Square Practice Packet | 60 Problems, a = 1, a ≠ 1 & a = 2 with Answer Keys

Help your students master completing the square and writing quadratics in vertex form, all in one printable download. Written by Brian McLogan, former high school math teacher of 14 years and creator of Free Math Videos, this packet builds the skill step by step, from a leading coefficient of 1 to factoring out a, to working with fractions. Use it as classwork, homework, a review packet or extra practice before a test.

What's included

• a = 1 Practice (20 problems): y = x² + bx ± 1 for b = 2 to 10, with whole-number answers
• a ≠ 1 Practice (20 problems): a = −1 to 5, where factoring out a always leaves ±2x, with whole-number answers
• a = 2 Practice (20 problems): the next step up, including vertex forms with fractions
• Ordered, Scrambled and Random sets for each part, so students build the pattern, break it, then mix it like a real test
• Answer keys: every answer in vertex form for all three parts

Topics covered

• Completing the square with a = 1
• Factoring out the leading coefficient, including a negative a
• Writing quadratics in vertex form y = a(x − h)² + k
• Working with fractional h and k values

Great for

• Algebra 1 and Algebra 2 teachers
• Homeschool families
• Tutors
• Students who want extra practice with vertex form

Format

Instant digital download. 13-page printable PDF (cover + 9 practice pages + 3 answer key pages), US letter size. No physical item ships.