Corner PatcherArcfolk · quadratics

Patches the missing corner of a square: completing the square.

Vertex Form by Completing the Square

Completing the square. In MathBound, the free Algebra I adventure game, Corner Patcher asks these problems, and the only way past is to solve them.

Part of Solving Quadratic Equations: chapter 10 of the standard course.

10 questions, no sign-up, nothing saved. Climbs from the basics to harder questions.

What you will practice

Vertex Form by Completing the Square. Rewrite x^2 + bx + c with an even b as (x + h)^2 + k.

Made by the game’s own question engine. Try each one, then open its steps.

When

y = x^{2} + 12 x + 4

is

written

as

y = (x - h)^{2} + k,

what

is

k ?

Show the worked steps

$Half$ $of$ $12$ $is$ $6;$ $its$ $square$ $is$ $36 .$
$Add$ $and$ $subtract$ $it:$ $the$ $square$ $is$ $(x + 6)^{2},$ $and$ $the$ $constant$ $becomes$ $- 32 .$
$So$ $(x + 6)^{2} - 32,$ $with$ $vertex$ $(- 6, - 32) .$

Answer: $- 32$

Complete

the

square

to

find

the

vertex

of

y = x^{2} - 2 x + 5 .

Show the worked steps

$Half$ $of$ $- 2$ $is$ $- 1;$ $its$ $square$ $is$ $1 .$
$Add$ $and$ $subtract$ $it:$ $the$ $square$ $is$ $(x - 1)^{2},$ $and$ $the$ $constant$ $becomes$ $4 .$
$So$ $(x - 1)^{2} + 4,$ $with$ $vertex$ $(1, 4) .$

Answer: $(1, 4)$

Complete

the

square

to

write

y = x^{2} - 10 x - 9

in

vertex

form.

Show the worked steps

$Half$ $of$ $- 10$ $is$ $- 5;$ $its$ $square$ $is$ $25 .$
$Add$ $and$ $subtract$ $it:$ $the$ $square$ $is$ $(x - 5)^{2},$ $and$ $the$ $constant$ $becomes$ $- 34 .$
$So$ $(x - 5)^{2} - 34,$ $with$ $vertex$ $(5, - 34) .$

Answer: $y = (x - 5)^{2} - 34$

Textbook	Lessons
Standard course	10.2
Big Ideas Math Algebra 1	9.4
Big Ideas Math Algebra 1 (2022)	9.4
CPM Core Connections Algebra	8.2.5
CPS Skyline Algebra	7.3-7.5
Eureka Math Algebra I (EngageNY)	4.11-4.13
Illustrative Mathematics Algebra 1	7.22-7.23
Illustrative Mathematics Algebra 1 (v.360)	8.22-8.23
Math Nation Algebra 1 (Florida B.E.S.T.)	8.5, 8.6, 8.7, 8.8
Reveal Algebra 1	11-5