This topic focuses on the skill of completing the square to rewrite quadratic equations in vertex form, where the leading coefficient is -1. There are seven problems provided, each presenting a different quadratic equation. The task for each problem is to transform the quadratic equation into its vertex form. The vertex form reveals the quadratic's vertex, assisting in finding maximum or minimum values, among other properties. Each problem provides multiple choices, challenging the learner to identify the correct vertex form. The activity is fundamental in understanding the transformations and properties of quadratic functions.

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 -1) Worksheet

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Quadratic Equation Complete Square - To Fully Complete (Coefficient -1)
1
Complete the square to convert this to vertex form
A LaTex expression showing y=-1x to the power of 2 +4x-8
a A LaTex expression showing y=-1(x-2) to the power of 2 -4
b A LaTex expression showing y=-1(x+2) to the power of 2 +4
c A LaTex expression showing y=-1(x+2) to the power of 2 -4
d A LaTex expression showing y=(x-2) to the power of 2 -4
2
Complete the square to convert this to vertex form
A LaTex expression showing y=-1x to the power of 2 +2x-5
a A LaTex expression showing y=-1(x-1) to the power of 2 -4
b A LaTex expression showing y=(x-1) to the power of 2 -4
c A LaTex expression showing y=-1(x+1) to the power of 2 -4
d A LaTex expression showing y=(x+1) to the power of 2 +4
3
Complete the square to convert this to vertex form
A LaTex expression showing y=-1x to the power of 2 +8x-12
a A LaTex expression showing y=-1(x+4) to the power of 2 -4
b A LaTex expression showing y=-1(x+4) to the power of 2 +4
c A LaTex expression showing y=-1(x-4) to the power of 2 -4
d A LaTex expression showing y=-1(x-4) to the power of 2 +4
4
Complete the square to convert this to vertex form
A LaTex expression showing y=-1x to the power of 2 -8x-15
a A LaTex expression showing y=-1(x-4) to the power of 2 +1
b A LaTex expression showing y=(x+4) to the power of 2 +1
c A LaTex expression showing y=-1(x+4) to the power of 2 -1
d A LaTex expression showing y=-1(x+4) to the power of 2 +1
5
Complete the square 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=(x+1) to the power of 2 +3
b A LaTex expression showing y=-1(x+1) to the power of 2 -3
c A LaTex expression showing y=-1(x-1) to the power of 2 +3
d A LaTex expression showing y=-1(x+1) to the power of 2 +3
6
Complete the square to convert this to vertex form
A LaTex expression showing y=-1x to the power of 2 -6x-10
a A LaTex expression showing y=-1(x+3) to the power of 2 -1
b A LaTex expression showing y=-1(x+3) to the power of 2 +1
c A LaTex expression showing y=-1(x-3) to the power of 2 +1
d A LaTex expression showing y=(x+3) to the power of 2 -1
7
Complete the square to convert this to vertex form
A LaTex expression showing y=-1x to the power of 2 -8x-14
a A LaTex expression showing y=-1(x+4) to the power of 2 +2
b A LaTex expression showing y=(x-4) to the power of 2 +2
c A LaTex expression showing y=(x+4) to the power of 2 -2
d A LaTex expression showing y=(x+4) to the power of 2 +2
8
Complete the square 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=(x+3) to the power of 2 +4
b A LaTex expression showing y=-1(x-3) to the power of 2 +4
c A LaTex expression showing y=-1(x+3) to the power of 2 +4
d A LaTex expression showing y=(x+3) to the power of 2 -4