Grade 9 · Math · Algebra 1

9th grade Complete the square, and solve by completing the square worksheet

6 printable versionsOn Level10 questions · answer keyFree · no account

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Complete the square, and solve by completing the square

Grade 9 Math Worksheet

NameDate

Circle the best answer, or write your answer on the line.

Noah solves x² + 6x = 16 with algebra tiles and one missing corner. What is the smaller solution?
Pia solves x² - 6x = 16 (the eraser is on standby). What is the larger solution?
Tala solves x² + 8x - 9 = 0 by completing the square. What is the smaller solution?
Zee plans a quilt pattern using x² - 10x - 24 = 0. What is the smaller solution?
In math club, Ari solves x² + 10x - 24 = 0. What is the smaller solution?
Bo's robot solves x² - 16x - 36 = 0 by completing the square. What is the larger solution?
Esme rewrites x² + 10x + 18 as (x + 5)² + k. What is k?
Jun rewrites x² - 6x + 4 as (x - 3)² + k to find the lowest row of its table. What is k?
Luz uses tiles to rewrite x² + 8x + 21 as (x + 4)² + k. What is k?
Milo's robot rewrites x² - 14x + 40 as (x - 7)² + k. What is k?

Complete the square, and solve by completing the square. Every version has 10 questions, and the answer key prints on the second page.

Standard: A-REI.B.4a, A-SSE.B.3b

complete the square: Add the corner number so the expression is a bracket squared.

corner: The small square (half of the x number, squared) that fills the gap.

perfect square: A bracket times itself, like (x + 5)².

vertex form: a(x - h)² + k: the lowest (or highest) row of the table.

both sides: Whatever is added on the left is added on the right.

Your child added half of the x number instead of half of it squared.

Your child squared the whole x number instead of half of it.

Your child put the whole x number in the bracket.

Ask: if each strip is 5 wide, how big is the corner square?

Ask: the 10x is split into two strips; how wide is each?

Ask: what is (x + 12)² multiplied out?

What is the most common mistake with complete the square, and solve by completing the square?

Your child added half of the x number instead of half of it squared.

How can I help my child with complete the square, and solve by completing the square?

Ask: if each strip is 5 wide, how big is the corner square?

Are these 9th grade math worksheets free to print?

Yes. All 6 printable versions at each level are free to print, with the answer key, and no account is needed.

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