This topic concentrates on the method of completing the square to transform quadratic equations into their vertex form. It focuses on quadratic equations where the coefficient of \(x^2\) is not 1 (denoted as Coefficient N in the worksheet). By practicing these problems, students learn how to identify and manipulate the terms in a quadratic equation, adjust for coefficients greater than 1, and accurately compute the constant term that completes the square. The worksheet includes multiple-choice questions where students must select the correct vertex form among several options.

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

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Quadratic Equation Complete Square - To Fully Complete (Coefficient N) Worksheet

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Quadratic Equation Complete Square - To Fully Complete (Coefficient N)
1
Complete the square to convert this to vertex form
A LaTex expression showing y=2x to the power of 2 -12x+20
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
2
Complete the square to convert this to vertex form
A LaTex expression showing y=2x to the power of 2 -16x+33
a A LaTex expression showing y=-2(x-4) to the power of 2 +1
b A LaTex expression showing y=-2(x+4) to the power of 2 +1
c A LaTex expression showing y=2(x-4) to the power of 2 +1
d A LaTex expression showing y=2(x+4) to the power of 2 +1
3
Complete the square to convert this to vertex form
A LaTex expression showing y=3x to the power of 2 +6x+6
a A LaTex expression showing y=3(x-1) to the power of 2 +3
b A LaTex expression showing y=-3(x+1) to the power of 2 +3
c A LaTex expression showing y=3(x+1) to the power of 2 +3
d A LaTex expression showing y=3(x+1) to the power of 2 -3
4
Complete the square to convert this to vertex form
A LaTex expression showing y=5x to the power of 2 -40x+81
a A LaTex expression showing y=5(x-4) to the power of 2 +1
b A LaTex expression showing y=-5(x+4) to the power of 2 -1
c A LaTex expression showing y=5(x-4) to the power of 2 -1
d A LaTex expression showing y=5(x+4) to the power of 2 +1
5
Complete the square to convert this to vertex form
A LaTex expression showing y=2x to the power of 2 -16x+34
a A LaTex expression showing y=2(x-4) to the power of 2 -2
b A LaTex expression showing y=2(x-4) to the power of 2 +2
c A LaTex expression showing y=2(x+4) to the power of 2 +2
d A LaTex expression showing y=2(x+4) to the power of 2 -2
6
Complete the square to convert this to vertex form
A LaTex expression showing y=2x to the power of 2 +4x+3
a A LaTex expression showing y=2(x+1) to the power of 2 +1
b A LaTex expression showing y=2(x-1) to the power of 2 +1
c A LaTex expression showing y=-2(x-1) to the power of 2 -1
d A LaTex expression showing y=2(x+1) to the power of 2 -1
7
Complete the square to convert this to vertex form
A LaTex expression showing y=5x to the power of 2 +40x+83
a A LaTex expression showing y=-5(x+4) to the power of 2 +3
b A LaTex expression showing y=-5(x+4) to the power of 2 -3
c A LaTex expression showing y=5(x+4) to the power of 2 +3
d A LaTex expression showing y=5(x+4) to the power of 2 -3
8
Complete the square to convert this to vertex form
A LaTex expression showing y=4x to the power of 2 -24x+34
a A LaTex expression showing y=-4(x+3) to the power of 2 -2
b A LaTex expression showing y=4(x-3) to the power of 2 -2
c A LaTex expression showing y=4(x+3) to the power of 2 -2
d A LaTex expression showing y=-4(x-3) to the power of 2 -2