Completing the Square Worksheet

Completing the Square Worksheet

Completing the Square Worksheet

Name: __________________________
Date: __________________________
Class: __________________________

Instructions

Complete the square to rewrite each quadratic expression or equation in vertex form. Show all your working.

A. Complete the Square

  1. (x^2 + 6x + ____)
  2. (x^2 + 10x + ____)
  3. (x^2 + 14x + ____)
  4. (x^2 – 8x + ____)
  5. (x^2 – 12x + ____)
  6. (x^2 + 4x + ____)
  7. (x^2 – 16x + ____)
  8. (x^2 + 18x + ____)
  9. (x^2 – 20x + ____)
  10. (x^2 + 2x + ____)

B. Rewrite in Vertex Form

Rewrite each quadratic in the form ((x-h)^2+k).

  1. (x^2 + 6x + 5)
  2. (x^2 + 8x + 7)
  3. (x^2 – 10x + 3)
  4. (x^2 – 12x + 8)
  5. (x^2 + 14x + 9)
  6. (x^2 – 16x + 12)
  7. (x^2 + 4x – 5)
  8. (x^2 – 6x + 2)
  9. (x^2 + 20x + 11)
  10. (x^2 – 18x + 4)

C. Solve by Completing the Square

  1. (x^2 + 6x + 5 = 0)
  2. (x^2 + 8x + 7 = 0)
  3. (x^2 – 10x + 21 = 0)
  4. (x^2 – 12x + 20 = 0)
  5. (x^2 + 14x + 45 = 0)
  6. (x^2 – 16x + 55 = 0)
  7. (x^2 + 4x – 12 = 0)
  8. (x^2 – 6x – 16 = 0)
  9. (x^2 + 10x + 9 = 0)
  10. (x^2 – 14x + 45 = 0)

D. Find the Vertex

Find the vertex of each parabola.

  1. (y=x^2+6x+5)
  2. (y=x^2-8x+3)
  3. (y=x^2+10x+7)
  4. (y=x^2-12x+4)
  5. (y=x^2+14x-2)
  6. (y=x^2-16x+8)
  7. (y=x^2+4x-9)
  8. (y=x^2-6x+1)
  9. (y=x^2+18x+5)
  10. (y=x^2-20x+10)

E. Challenge Questions

  1. (2x^2+8x+3=0)
  2. (2x^2-12x+5=0)
  3. (3x^2+12x-7=0)
  4. (3x^2-18x+4=0)
  5. (4x^2+16x+3=0)
  6. (4x^2-24x+5=0)
  7. Find the vertex of (y=2x^2+12x+7).
  8. Find the vertex of (y=3x^2-18x+10).
  9. Solve (x^2+4x-5=0) by completing the square.
  10. Solve (x^2-10x+13=0) by completing the square.

Answer Key

A.

  1. 9
  2. 25
  3. 49
  4. 16
  5. 36
  6. 4
  7. 64
  8. 81
  9. 100
  10. 1

B.

  1. ((x+3)^2-4)
  2. ((x+4)^2-9)
  3. ((x-5)^2-22)
  4. ((x-6)^2-28)
  5. ((x+7)^2-40)
  6. ((x-8)^2-52)
  7. ((x+2)^2-9)
  8. ((x-3)^2-7)
  9. ((x+10)^2-89)
  10. ((x-9)^2-77)

C.

  1. (x=-1,-5)
  2. (x=-1,-7)
  3. (x=3,7)
  4. (x=2,10)
  5. (x=-5,-9)
  6. (x=5,11)
  7. (x=2,-6)
  8. (x=8,-2)
  9. (x=-1,-9)
  10. (x=5,9)

D.

  1. ((-3,-4))
  2. ((4,-13))
  3. ((-5,-18))
  4. ((6,-32))
  5. ((-7,-51))
  6. ((8,-56))
  7. ((-2,-13))
  8. ((3,-8))
  9. ((-9,-76))
  10. ((10,-90))

E.

  1. (x=-2\pm\frac{\sqrt{10}}{2})
  2. (x=3\pm\frac{\sqrt{26}}{2})
  3. (x=-2\pm\frac{\sqrt{30}}{3})
  4. (x=3\pm\frac{\sqrt{23}}{3})
  5. (x=-2\pm\frac{\sqrt{13}}{2})
  6. (x=3\pm\frac{\sqrt{31}}{2})
  7. Vertex: ((-3,-11))
  8. Vertex: ((3,-17))
  9. (x=1,-5)
  10. (x=5\pm2\sqrt3)