This math topic focuses on transforming quadratic equations to prepare them for completing the square, specifically when the leading coefficient of the quadratic term is negative one (-1). It targets skills in factoring out the negative coefficient from the x terms and rearranging the equation. Each problem presents a different quadratic equation and multiple choice answers, where students select the correctly reformed equation ready for completing the square. It is an integral part of learning about quadratic equations and transitioning to vertex form.

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

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

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Quadratic Equation Complete Square - To Removed Coefficient (Coeffici...
1
Remove the leading coefficient from the x terms to be ready to complete the square
A LaTex expression showing y=-1x to the power of 2 +8x-19
a A LaTex expression showing y=-1(x to the power of 2 -8x)-19
b A LaTex expression showing y=-1(x to the power of 2 -8x)-21
c A LaTex expression showing y=-1(x to the power of 2 -10x)-19
d A LaTex expression showing y=-1(x to the power of 2 +8x)-19
e A LaTex expression showing y=-1(x to the power of 2 -8x)-20
2
Remove the leading coefficient from the x terms to be ready to complete the square
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 -1x)-5
b A LaTex expression showing y=-1(x to the power of 2 +6x)-5
c A LaTex expression showing y=-1(x to the power of 2 -6x)-4
d A LaTex expression showing y=-1(x to the power of 2 -6x)-5
e A LaTex expression showing y=-1(x to the power of 2 -2x)-5
3
Remove the leading coefficient from the x terms to be ready to complete the square
A LaTex expression showing y=-1x to the power of 2 -6x-8
a A LaTex expression showing y=-1(x to the power of 2 -6x)-8
b A LaTex expression showing y=-1(x to the power of 2 +6x)-7
c A LaTex expression showing y=-1(x to the power of 2 +6x)-10
d A LaTex expression showing y=-1(x to the power of 2 +5x)-8
e A LaTex expression showing y=-1(x to the power of 2 +6x)-8
4
Remove the leading coefficient from the x terms to be ready to complete the square
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)-1
b A LaTex expression showing y=-1(x to the power of 2 -4x)-2
c A LaTex expression showing y=-1(x to the power of 2 -4x)+1
d A LaTex expression showing y=-1(x to the power of 2 -4x)-1
e A LaTex expression showing y=-1(x to the power of 2 -4x)-0
5
Remove the leading coefficient from the x terms to be ready to complete the square
A LaTex expression showing y=-1x to the power of 2 -6x-11
a A LaTex expression showing y=-1(x to the power of 2 +6x)-13
b A LaTex expression showing y=-1(x to the power of 2 +6x)-9
c A LaTex expression showing y=-1(x to the power of 2 +6x)-11
d A LaTex expression showing y=-1(x to the power of 2 -6x)-11
e A LaTex expression showing y=-1(x to the power of 2 +6x)-10
6
Remove the leading coefficient from the x terms to be ready to complete the square
A LaTex expression showing y=-1x to the power of 2 +2x-5
a A LaTex expression showing y=-1(x to the power of 2 -2x)-5
b A LaTex expression showing y=-1(x to the power of 2 +2x)-5
c A LaTex expression showing y=-1(x to the power of 2 -2x)-3
d A LaTex expression showing y=-1(x to the power of 2 -2x)-4
e A LaTex expression showing y=-1(x to the power of 2 -2x)-7
7
Remove the leading coefficient from the x terms to be ready to complete the square
A LaTex expression showing y=-1x to the power of 2 +6x-8
a A LaTex expression showing y=-1(x to the power of 2 +6x)-8
b A LaTex expression showing y=-1(x to the power of 2 -6x)-6
c A LaTex expression showing y=-1(x to the power of 2 -6x)-9
d A LaTex expression showing y=-1(x to the power of 2 -6x)-8
e A LaTex expression showing y=-1(x to the power of 2 -6x)-10
8
Remove the leading coefficient from the x terms to be ready to complete the square
A LaTex expression showing y=-1x to the power of 2 +4x-8
a A LaTex expression showing y=-1(x to the power of 2 -9x)-8
b A LaTex expression showing y=-1(x to the power of 2 -3x)-8
c A LaTex expression showing y=-1(x to the power of 2 -4x)-8
d A LaTex expression showing y=-1(x to the power of 2 -4x)-7
e A LaTex expression showing y=-1(x to the power of 2 +4x)-8