Completing the Square Practice Problems

Here you will find a concise set of completing the square practice problems. Visit this page directly at hunkim.com/complete

1. Basic complete-the-square problem
   x^2+4x-1
   
2. Basic problem with a negative coefficient of x
   x^2-12x+3
   
3. Basic problem using a variable other than x
   a^2-2a-5
   
4. Basic problem with “y=”
   Complete the square on y=x^2-6x+3
   
5. Basic problem using function notation “h(t)=”
   Complete the square on h(t)=t^2-4t-2
   
6. Review the five problems above and identify the coordinates of the vertex.
   
7. Complete the square when there is no constant term
   y=x^2-10x
   
8. Complete the square involving fractions
   y=x^2-x+1
   
9. Complete the square involving a coefficient other than 1
   y=2x^2-4x-3
   
10. Complete the square then solve by setting y=0
    1. y=x^2+2x-8
    2. y=x^2-x-5
    3. y=2x^2-6x-7
       
11. Complete the square where a is a fraction
    y=\frac{2}{3}x^2-\frac{x}{2}-0.2
    
12. Complete the square when there are no numbers
    y=ax^2+bx+c

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