This math topic focuses on completing the square for quadratic equations with a leading coefficient of negative one (-1) to facilitate their conversion into vertex form. The skill practiced here is crucial for understanding how to manipulate quadratic expressions and derive their vertex forms, an introductory concept to quadratic equations and vertex forms. The exercise involves multiple-choice questions, each presenting a quadratic equation along with several options to choose the correctly completed square expression.

Work on practice problems directly here, or download the printable pdf worksheet to practice offline.

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Quadratic Equation Complete Square - To Partially Complete (Coefficient -1) Worksheet

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Quadratic Equation Complete Square - To Partially Complete (Coefficient -1)
1
Complete the square to be ready to convert this to vertex form
A LaTex expression showing y=-1x to the power of 2 -2x+1
a A LaTex expression showing y=-1(x to the power of 2 +2x+6)+1+1
b A LaTex expression showing y=-1(x to the power of 2 +2x+1)+1+1
c A LaTex expression showing y=-1(x to the power of 2 +1x+1)+1+1
d A LaTex expression showing y=-1(x to the power of 2 +2x+1)-1+1
e A LaTex expression showing y=-1(x to the power of 2 +2x-3)+1+1
2
Complete the square to be ready to convert this to vertex form
A LaTex expression showing y=-1x to the power of 2 -6x-5
a A LaTex expression showing y=-1(x to the power of 2 +6x+9)+9-5
b A LaTex expression showing y=-1(x to the power of 2 +6x+6)+9-5
c A LaTex expression showing y=-1(x to the power of 2 +6x+14)+9-5
d A LaTex expression showing y=-1(x to the power of 2 +6x+9)-9-5
e A LaTex expression showing y=-1(x to the power of 2 +6x+11)+9-5
3
Complete the square to be ready to convert this to vertex form
A LaTex expression showing y=-1x to the power of 2 -8x-20
a A LaTex expression showing y=-1(x to the power of 2 +8x+15)+16-20
b A LaTex expression showing y=-1(x to the power of 2 +8x+16)+16-20
c A LaTex expression showing y=-1(x to the power of 2 +11x+16)+16-20
d A LaTex expression showing y=-1(x to the power of 2 +8x+16)-16-20
e A LaTex expression showing y=-1(x to the power of 2 +8x+16)+11-20
4
Complete the square to be ready to convert this to vertex form
A LaTex expression showing y=-1x to the power of 2 -8x-13
a A LaTex expression showing y=-1(x to the power of 2 +8x+13)+16-13
b A LaTex expression showing y=-1(x to the power of 2 +8x+15)+16-13
c A LaTex expression showing y=-1(x to the power of 2 +8x+16)+16-13
d A LaTex expression showing y=-1(x to the power of 2 +8x+16)-16-13
e A LaTex expression showing y=-1(x to the power of 2 +8x+16)-21-13
5
Complete the square to be ready to convert this to vertex form
A LaTex expression showing y=-1x to the power of 2 -8x-18
a A LaTex expression showing y=-1(x to the power of 2 +8x+16)+16-18
b A LaTex expression showing y=-1(x to the power of 2 +8x+16)-12-18
c A LaTex expression showing y=-1(x to the power of 2 +8x+16)+13-18
d A LaTex expression showing y=-1(x to the power of 2 +8x+21)+16-18
e A LaTex expression showing y=-1(x to the power of 2 +8x+18)+16-18
6
Complete the square to be ready to convert this to vertex form
A LaTex expression showing y=-1x to the power of 2 +2x+2
a A LaTex expression showing y=-1(x to the power of 2 -2x-4)+1+2
b A LaTex expression showing y=-1(x to the power of 2 -2x+1)-1+2
c A LaTex expression showing y=-1(x to the power of 2 -2x+1)+1+2
d A LaTex expression showing y=-1(x to the power of 2 -2x-2)+1+2
e A LaTex expression showing y=-1(x to the power of 2 -2x+1)-3+2
7
Complete the square to be ready to convert this to vertex form
A LaTex expression showing y=-1x to the power of 2 +4x-1
a A LaTex expression showing y=-1(x to the power of 2 -4x+4)-4-1
b A LaTex expression showing y=-1(x to the power of 2 -4x-1)+4-1
c A LaTex expression showing y=-1(x to the power of 2 -4x+4)+4-1
d A LaTex expression showing y=-1(x to the power of 2 -4x+4)-3-1
e A LaTex expression showing y=-1(x to the power of 2 -4x+8)+4-1
8
Complete the square to be ready to convert this to vertex form
A LaTex expression showing y=-1x to the power of 2 -4x-7
a A LaTex expression showing y=-1(x to the power of 2 +4x+4)-4-7
b A LaTex expression showing y=-1(x to the power of 2 +4x+4)+4-7
c A LaTex expression showing y=-1(x to the power of 2 +4x+4)+8-7
d A LaTex expression showing y=-1(x to the power of 2 +4x+7)+4-7
e A LaTex expression showing y=-1(x to the power of 2 +4x+4)-9-7