Complete the Square

Complete the Square

Multiple Choice

Factor the following:

$$x^2+14x+49$$

• $$\left(x-7\right)\left(x+7\right)$$

• $$\left(x-7\right)\left(x-7\right)$$

• $$\left(x+7\right)\left(x+7\right)$$

Multiple Choice

Factor the following:

$$x^2-6x+9$$

• $$\left(x-3\right)\left(x+3\right)$$

• $$\left(x-3\right)\left(x-3\right)$$

• $$\left(x+3\right)\left(x+3\right)$$

Multiple Choice

Factor the following:

$$x^2-10x+25$$

• $$\left(x-5\right)\left(x-5\right)$$

• $$\left(x+5\right)\left(x-5\right)$$

• $$\left(x-5\right)\left(x+5\right)$$

Multiple Choice

Factor the following:

$$x^2+8x+16$$

• $$\left(x+4\right)^2$$

• $$\left(x-4\right)^2$$

• $$x^2-4$$

• $$\left(x-4\right)\left(x+4\right)$$

A perfect sqaure trinomial is obtained by squaring a binomial expression. We will create perfect square trinomials to complete the square.

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Perfect Square

Trinomials

Completing the Square

A method to solve quadratic functions

When you cannot factor a quadratic function, and it is impracticle to graph the function, you can complete the square. This method is best used when:

1. There is no lead coefficient.

2. The coefficient on the "b" term is even.

You can ALWAYS use complete the square to solve a quadratic function.

Multiple Choice

What do you do to the b value to correctly complete the square?

• square it

• divide it by 2 and square the result

• divide it by 2 and take the square root of the result

• divide it by 2 only

Multiple Choice

Complete the square for

x² + 12x + ___= ___

(find the missing number in the blanks)

• x² + 12x + 144=144

• x² + 12x + 36=36

• x² + 12x - 36=-36

• x² + +12x - 144=-144

Multiple Choice

Complete the square for

x² - 14x + __=__

(find the missing value that goes in the blank)

• - 196

• 49

• - 49

• 28

Multiple Choice

Complete the square for

x² + 6x + __=__

(find the missing value that goes in the blank)

• 9

• 12

• 36

• - 9

Multiple Choice

What value of c would complete the square?

x² +8x + c = c

• 4

• 16

• 64

• -16

Multiple Choice

What value of c would complete the square?

x² + 2x + c = c

• 2

• 4

• -2

• 1

Multiple Choice

Find the missing value to create a perfect square trinomial and complete the square:

x² + 26x + __=__ 

• 13

• 136

• 169

• 26

Reorder

Put the steps to Completing the Square in the correct order

• Move constants to one side

• add $$\left(\frac{b}{2}\right)^2$$ to both sides

• Factor the trinomial

• Take the square root of both sides.

• Solve both cases.

1

2

3

4

5

• 1
• 2
• 3
• 4
• 5

Multiple Choice

What is the first step to completing the square for this equation?

0 = x² + 10x + 21

• Set the equation equal to zero

• Divide 10 by 2 and add the result to both sides

• Add x² and 10x together

• Subtract 21 on both sides

Multiple Choice

What do you do to the "b" value to correctly complete the square?

• square it

• divide it by 2 and square the result

• divide it by 2 and take the square root of the result

• divide it by 2 only

Multiple Choice

 Complete the square but do not solve.

$$x^2+10x\ -11=0$$

• $$\left(x+5\right)^2=36$$  

• $$\left(x+5\right)^2=25$$  

• $$\left(x+10\right)^2=100$$  

• $$\left(x+10\right)^2=111$$  

Multiple Choice

To solve by completing the square, what needs to be moved in this equation?
x² = 9 - 4x

• the -4x

• the 9

• the x²

Multiple Choice

When factoring
x² - 4x + 4 = 20,
what goes in the blank?
(x - __ )² = 20

• 4

• 2

• 8

• 20

Multiple Choice

Solve for x by taking the Square Root:

(x+6)² = 49

• x = 7 and 12

• x = ±7

• x = 1 and -13

• x = 43 and -55

Multiple Choice

What is $$\sqrt[]{8}$$ simplified?

• $$2\sqrt[]{2}$$

• $$4\sqrt[]{2}$$

• $$2i\sqrt[]{2}$$

• $$2\sqrt[]{2i}$$

Multiple Choice

Solve by completing the square:
k² − 12k + 23 = 0

• {6 + √13, 6 - √13}

• {-6 + √13, -6 - √13}

• {6 + √59, 6 - √59}

• {-6 + √59, -6 - √59}

Multiple Choice

Solve by completing the square:

v² + 6v − 59 = 0

• {-5 + √50, -5 - √50}

• {5 + √50, 5 - √50}

• {-3 + √68, -3 - √68}

• {3 + √68, 3 - √68}

Multiple Choice

True or false:

When the solution is imaginary, the quadratic crosses the x-axis

• True

• False

Match

Match the following

• $$f\left(x\right)=a\left(x-h\right)^2+k$$

• $$f\left(x\right)=ax^2+ba+c$$

• $$d\ =\ b^2-4ac$$

• $$x=\frac{-b}{2a}$$

• $$f\left(x\right)=\left(x-r\right)\left(x-s\right)$$

vertex form of a quadratic

standard form of a quadratic

formula for discriminant

equation for axis of symmetry

factored form of a quadratic

• vertex form of a quadratic

• standard form of a quadratic

• formula for discriminant

• equation for axis of symmetry

• factored form of a quadratic

Poll

Did you know there were instructional videos for each concept in the unit modules in Canvas?

• Yes

• No

Poll

Overall, my knowledge of quadratics is...