This math topic helps students practice the skill of completing the square in quadratic equations, specifically focusing on rewriting equations with a negative coefficient on the quadratic term. Students learn to factor out the negative coefficient from the quadratic and linear terms before completing the square. Each problem presents a quadratic expression and multiple rewriting options, from which the correct form must be identified. These exercises are vital for understanding transformations of quadratic functions into vertex form, reinforcing algebraic manipulation and problem-solving skills in the context of quadratic equations.

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Quadratic Equation Complete Square - To Removed Coefficient (Coefficient -N) 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=-2x to the power of 2 -12x-22
a A LaTex expression showing y=-2(x to the power of 2 +12x)-22
b A LaTex expression showing y=-2(x to the power of 2 +6x)-20
c A LaTex expression showing y=-2(x to the power of 2 +6x)-21
d A LaTex expression showing y=-2(x to the power of 2 +6x)-23
e A LaTex expression showing y=-2(x to the power of 2 +6x)-22
2
Remove the leading coefficient from the x terms to be ready to complete the square
A LaTex expression showing y=-5x to the power of 2 -30x-46
a A LaTex expression showing y=-5(x to the power of 2 +6x)-45
b A LaTex expression showing y=-5(x to the power of 2 +6x)-46
c A LaTex expression showing y=-5(x to the power of 2 +1x)-46
d A LaTex expression showing y=-5(x to the power of 2 -6x)-46
e A LaTex expression showing y=-5(x to the power of 2 +30x)-46
3
Remove the leading coefficient from the x terms to be ready to complete the square
A LaTex expression showing y=-3x to the power of 2 +12x-15
a A LaTex expression showing y=-3(x to the power of 2 -4x)-16
b A LaTex expression showing y=-3(x to the power of 2 -4x)-15
c A LaTex expression showing y=-3(x to the power of 2 -4x)-14
d A LaTex expression showing y=-3(x to the power of 2 -4x)-13
e A LaTex expression showing y=-3(x to the power of 2 -12x)-15
4
Remove the leading coefficient from the x terms to be ready to complete the square
A LaTex expression showing y=-3x to the power of 2 +24x-45
a A LaTex expression showing y=-3(x to the power of 2 -8x)-45
b A LaTex expression showing y=-3(x to the power of 2 -8x)-46
c A LaTex expression showing y=-3(x to the power of 2 -8x)-43
d A LaTex expression showing y=-3(x to the power of 2 +8x)-45
e A LaTex expression showing y=-3(x to the power of 2 -24x)-45
5
Remove the leading coefficient from the x terms to be ready to complete the square
A LaTex expression showing y=-4x to the power of 2 -24x-39
a A LaTex expression showing y=-4(x to the power of 2 +6x)-39
b A LaTex expression showing y=-4(x to the power of 2 -6x)-39
c A LaTex expression showing y=-4(x to the power of 2 +6x)-41
d A LaTex expression showing y=-4(x to the power of 2 +6x)-38
e A LaTex expression showing y=-4(x to the power of 2 +24x)-39
6
Remove the leading coefficient from the x terms to be ready to complete the square
A LaTex expression showing y=-3x to the power of 2 -12x-10
a A LaTex expression showing y=-3(x to the power of 2 +4x)-10
b A LaTex expression showing y=-3(x to the power of 2 +4x)-9
c A LaTex expression showing y=-3(x to the power of 2 +4x)-12
d A LaTex expression showing y=-3(x to the power of 2 -4x)-10
e A LaTex expression showing y=-3(x to the power of 2 +12x)-10
7
Remove the leading coefficient from the x terms to be ready to complete the square
A LaTex expression showing y=-4x to the power of 2 +8x-8
a A LaTex expression showing y=-4(x to the power of 2 -2x)-8
b A LaTex expression showing y=-4(x to the power of 2 -8x)-8
c A LaTex expression showing y=-4(x to the power of 2 +2x)-8
d A LaTex expression showing y=-4(x to the power of 2 -0x)-8
e A LaTex expression showing y=-4(x to the power of 2 -2x)-7
8
Remove the leading coefficient from the x terms to be ready to complete the square
A LaTex expression showing y=-2x to the power of 2 +12x-14
a A LaTex expression showing y=-2(x to the power of 2 -6x)-13
b A LaTex expression showing y=-2(x to the power of 2 -12x)-14
c A LaTex expression showing y=-2(x to the power of 2 -6x)-14
d A LaTex expression showing y=-2(x to the power of 2 -6x)-16
e A LaTex expression showing y=-2(x to the power of 2 +6x)-14