Solve Quadratics by Competing the Square Lesson

​Solve Quadratics by Completing the Square

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Multiple Choice

Given the equation $$x^2+18x=0$$  how do you find the number to add to both sides to help you complete the square?  #1

• Divide 18 by 2, then square that number and add it to both sides of the equation

• Square 18 and then add it both sides of the equation

• It already is a perfect square

• Subtract 18x from both sides and then divide both sides by x to find the answer

Multiple Choice

Answer the question. #3

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Reorder

Put the steps to Complete the Square in the correct order. #29

• 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.

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5

• 1
• 2
• 3
• 4
• 5

Multiple Choice

What is the arrow pointing at? How can you use this value to determine the minimum/maximum values? #33

• The arrow is pointing at the y-intercept. The y value of this point is equivalent to the maximum/minimum 

• The arrow is pointing at the vertex. The x value of this point is equivalent to the maximum/minimum

• The arrow is pointing at the solution. The y value of this point is equivalent to the maximum and the x value is equivalent to the minimum

• The arrow is pointing at the vertex. The y value is equivalent to the minimum/maximum

Multiple Choice

When factoring this equation: $$x^2-4x+4=20$$   ...what value should p be equal to?   $$\left(x-p\right)^2=20$$  #2

• 4

• 2

• 8

• 20

Multiple Choice

Find the vertex of this quadratic equation: $$y=x^2+8x+18$$  #6

• (4,2)

• (-4,2)

• (8,18)

• (-4,-2)

• (4,-2)

Multiple Choice

Find the vertex of this quadratic equation: $$y=x^2-2x-2$$  #8

• (2,3)

• (2,-2)

• (-1,-3)

• (1,-3)

• (-1,3)

Multiple Select

Check all of the following which are TRUE for the parabola that would result from graphing this equation: $$y=-2\left(x+4\right)^2-5$$  #11

• Opens up

• Opens down

• Vertex is (4,-5)

• y-intercept is (0,-37)

• Has 2 x-intercepts

Multiple Select

Check all of the following which are TRUE for the parabola that would result from graphing this equation: $$y=2\left(x-5\right)^2+15$$  #12

• Opens up

• Opens down

• Vertex is (5,15)

• y-intercept is (0,65)

• Has 2 x-intercepts

Multiple Choice

What is the y value of the y-intercept of this equation? #14 $$y=-2\left(x+3\right)^2+16$$  

• 34

• -3

• 16

• -2

• 2

Multiple Choice

Complete the square for the equation: #18

$$x^2+6x-4=0$$  

• $$\left(x+3\right)^2=4$$  

• $$\left(x-3\right)^2=4$$  

• $$\left(x+3\right)^2=13$$  

• $$\left(x-3\right)^2=13$$  

Multiple Choice

Complete the square for the equation: #19

$$x^2-10x+7=0$$  

• $$\left(x-5\right)^2=18$$  

• $$\left(x+5\right)^2=18$$   

• $$\left(x-5\right)^2=-7$$    

•   $$\left(x+5\right)^2=-7$$  

Multiple Choice

Solve by completing the square. #20

$$x^2-8x-20=0$$  

• $$x=\left\{-2,\ 10\right\}$$  

• $$x=\left\{-10,\ 2\right\}$$  

• $$x=\left\{-20,\ -8\right\}$$  

• $$x=\left\{8,\ 20\right\}$$  

Multiple Choice

Solve by completing the square. #21

$$x^2-6x-59=0$$  

• $$x=\left\{\pm2\sqrt{17}+3\right\}$$  

• $$x=\left\{\pm17\sqrt{2}+3\right\}$$  

• $$x=\left\{\pm2\sqrt{17}-3\right\}$$  

• $$x=\left\{\pm17\sqrt{2}-3\right\}$$  

Multiple Choice

$$x^2-36x+2=0$$  Complete the Square and Solve for "x." #23

• $$x=18\pm\sqrt{322}$$  

• $$x=-18\pm\sqrt{326}$$  

• $$x=18\pm\sqrt{326}$$  

• $$x=-18\pm\sqrt{322}$$