This math topic focuses on converting quadratic equations from a standard form to a vertex form by completing the square. The problems entail adjusting quadratic equations with negative coefficients and include both solving for the square and simplifying the expression to its vertex form. Each question presents a different quadratic equation and multiple-choice answers, challenging the learner to pick the correct vertex form of the quadratic equation illustrated.

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

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Quadratic Equation Complete Square - Partially to Fully Complete (Coefficient -N) Worksheet

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Quadratic Equation Complete Square - Partially to Fully Complete (Coefficient -N)
1
Solve the square polynomial to finish converting this to vertex form
A LaTex expression showing y=-4(x to the power of 2 +2x+1)+4-3
a A LaTex expression showing y=4(x-1) to the power of 2 +1
b A LaTex expression showing y=-4(x+1) to the power of 2 +1
c A LaTex expression showing y=4(x+1) to the power of 2 -1
d A LaTex expression showing y=-4(x-1) to the power of 2 +1
2
Solve the square polynomial to finish converting this to vertex form
A LaTex expression showing y=-5(x to the power of 2 -2x+1)+5-4
a A LaTex expression showing y=-5(x-1) to the power of 2 +1
b A LaTex expression showing y=-5(x-1) to the power of 2 -1
c A LaTex expression showing y=5(x-1) to the power of 2 +1
d A LaTex expression showing y=5(x+1) to the power of 2 +1
3
A LaTex expression showing y=-5(x to the power of 2 -8x+16)+80-84
Solve the square polynomial to finish converting this to vertex form
a A LaTex expression showing y=5(x-4) to the power of 2 +4
b A LaTex expression showing y=-5(x-4) to the power of 2 -4
c A LaTex expression showing y=5(x-4) to the power of 2 -4
d A LaTex expression showing y=-5(x+4) to the power of 2 -4
4
A LaTex expression showing y=-2(x to the power of 2 -6x+9)+18-16
Solve the square polynomial to finish converting this to vertex form
a A LaTex expression showing y=-2(x+3) to the power of 2 +2
b A LaTex expression showing y=-2(x-3) to the power of 2 +2
c A LaTex expression showing y=2(x+3) to the power of 2 +2
d A LaTex expression showing y=2(x-3) to the power of 2 +2
5
A LaTex expression showing y=-5(x to the power of 2 -6x+9)+45-47
Solve the square polynomial to finish converting this to vertex form
a A LaTex expression showing y=-5(x-3) to the power of 2 +2
b A LaTex expression showing y=5(x-3) to the power of 2 -2
c A LaTex expression showing y=5(x+3) to the power of 2 -2
d A LaTex expression showing y=-5(x-3) to the power of 2 -2
6
Solve the square polynomial to finish converting this to vertex form
A LaTex expression showing y=-3(x to the power of 2 +2x+1)+3-1
a A LaTex expression showing y=-3(x+1) to the power of 2 +2
b A LaTex expression showing y=-3(x+1) to the power of 2 -2
c A LaTex expression showing y=3(x-1) to the power of 2 +2
d A LaTex expression showing y=3(x+1) to the power of 2 +2
7
A LaTex expression showing y=-3(x to the power of 2 -8x+16)+48-45
Solve the square polynomial to finish converting this to vertex form
a A LaTex expression showing y=-3(x-4) to the power of 2 -3
b A LaTex expression showing y=-3(x-4) to the power of 2 +3
c A LaTex expression showing y=3(x+4) to the power of 2 +3
d A LaTex expression showing y=-3(x+4) to the power of 2 +3
8
A LaTex expression showing y=-3(x to the power of 2 +8x+16)+48-49
Solve the square polynomial to finish converting this to vertex form
a A LaTex expression showing y=3(x+4) to the power of 2 +1
b A LaTex expression showing y=-3(x+4) to the power of 2 -1
c A LaTex expression showing y=-3(x+4) to the power of 2 +1
d A LaTex expression showing y=-3(x-4) to the power of 2 +1