Standard to Tiles to Vertex

Completing the Square:
From Standard form
to Tiles
to Vertex Form

By Mr. Elm

Part 1: Making Connections

Multiple Choice

Which standard form quadratic matches this diagram?

• $$x^2+6x+3$$

• $$x^2+6x+4$$

• $$x^2+4x+4$$

• $$x^2+4x+3$$

Multiple Choice

Which diagram matches this standard form quadratic?

$$x^2+4x+1$$

Multiple Choice

Which expression matches this tile diagram?

• $$\left(x+1\right)^2$$

• $$\left(x+2\right)^2$$

• $$\left(x+3\right)^2$$

• $$\left(x+4\right)^2$$

Multiple Choice

Which tile diagram matches this expression?

$$\left(x+3\right)^2$$

Multiple Choice

Which vertex form expression matches this diagram?

• $$\left(x+3\right)^2-1$$

• $$\left(x+3\right)^2-2$$

• $$\left(x+3\right)^2-3$$

• $$\left(x+3\right)^2-4$$

Multiple Choice

Which diagram matches this vertex form expression?

$$\left(x+2\right)^2-1$$

Part 2, Problems

Problem 1
x²+6x+5

Multiple Choice

Which diagram matches this standard form quadratic?

$$x^2+6x+5$$

Multiple Choice

Which vertex form expression matches this diagram?

• $$\left(x+3\right)^2-3$$

• $$\left(x+3\right)^2-4$$

• $$\left(x+3\right)^2-5$$

• $$\left(x+3\right)^2-6$$

Problem 2
x²+4x+2

Multiple Choice

Which diagram matches this standard form quadratic?

$$x^2+4x+2$$

Multiple Choice

Which vertex form expression matches this diagram?

• $$\left(x+2\right)^2-1$$

• $$\left(x+2\right)^2-2$$

• $$\left(x+4\right)^2-1$$

• $$\left(x+4\right)^2-2$$

Problem 3
x²+6x+10

Multiple Choice

Which diagram matches this standard form quadratic?

$$x^2+6x+10$$

Multiple Choice

Which vertex form expression matches this diagram?

• $$\left(x+3\right)^2+1$$

• $$\left(x+3\right)^2+2$$

• $$\left(x+6\right)^2+1$$

• $$\left(x+6\right)^2+2$$

Problem 4
x²-4x+3

Multiple Choice

Which diagram matches this standard form quadratic?

$$x^2-4x+3$$

Multiple Choice

Which vertex form expression matches this diagram?

• $$\left(x-2\right)^2-1$$

• $$\left(x-4\right)^2-1$$

• $$\left(x-2\right)^2+3$$

• $$\left(x-4\right)^2+3$$

Problem 5
x²-6x+11

Multiple Choice

Which diagram matches this standard form quadratic?

$$x^2-6x+11$$

Multiple Choice

Which vertex form expression matches this diagram?

• $$\left(x-3\right)^2+1$$

• $$\left(x-3\right)^2+2$$

• $$\left(x-6\right)^2+1$$

• $$\left(x-6\right)^2+2$$