Quadratic Equation Complete Square - Partially to Fully Complete (Coefficient 1)

Level 1

This math topic focuses on solving quadratic equations by completing the square. The worksheet involves converting quadratic expressions into vertex form. Students are given quadratic expressions with a leading coefficient of 1, and they are required to manipulate these expressions to achieve the completed square form. This forms a basis for understanding the structure of quadratic equations in their vertex form and how changes in the equation reflect graphically. Each problem presents multiple-choice answers for the students to select the correctly completed square equation. This topic is a foundational component of understanding quadratic equations and their graphical representations.

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 1) Worksheet

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Quadratic Equation Complete Square - Partially to Fully Complete (Coe...
1
Solve the square polynomial to finish factoring
A LaTex expression showing y=(x to the power of 2 -4x+4)-4
a A LaTex expression showing y=-1(x-2) to the power of 2 -4
b A LaTex expression showing y=(x-2) to the power of 2 +4
c A LaTex expression showing y=(x-2) to the power of 2 -4
d A LaTex expression showing y=(x+2) to the power of 2 -4
2
Solve the square polynomial to finish factoring
A LaTex expression showing y=(x to the power of 2 +2x+1)-1-3
a A LaTex expression showing y=(x+1) to the power of 2 -4
b A LaTex expression showing y=-1(x-1) to the power of 2 -4
c A LaTex expression showing y=(x-1) to the power of 2 -4
d A LaTex expression showing y=(x+1) to the power of 2 +4
3
Solve the square polynomial to finish factoring
A LaTex expression showing y=(x to the power of 2 +4x+4)-4+6
a A LaTex expression showing y=(x-2) to the power of 2 -2
b A LaTex expression showing y=(x-2) to the power of 2 +2
c A LaTex expression showing y=(x+2) to the power of 2 +2
d A LaTex expression showing y=-1(x+2) to the power of 2 -2
4
Solve the square polynomial to finish factoring
A LaTex expression showing y=(x to the power of 2 +6x+9)-9+11
a A LaTex expression showing y=(x+3) to the power of 2 -2
b A LaTex expression showing y=-1(x+3) to the power of 2 +2
c A LaTex expression showing y=(x+3) to the power of 2 +2
d A LaTex expression showing y=(x-3) to the power of 2 +2
5
Solve the square polynomial to finish factoring
A LaTex expression showing y=(x to the power of 2 +4x+4)-4
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=(x+2) to the power of 2 -4
d A LaTex expression showing y=(x-2) to the power of 2 +4
6
Solve the square polynomial to finish factoring
A LaTex expression showing y=(x to the power of 2 -2x+1)-1-1
a A LaTex expression showing y=-1(x-1) to the power of 2 +2
b A LaTex expression showing y=(x-1) to the power of 2 +2
c A LaTex expression showing y=(x+1) to the power of 2 -2
d A LaTex expression showing y=(x-1) to the power of 2 -2
7
Solve the square polynomial to finish factoring
A LaTex expression showing y=(x to the power of 2 -2x+1)-1+3
a A LaTex expression showing y=-1(x-1) to the power of 2 -2
b A LaTex expression showing y=-1(x-1) to the power of 2 +2
c A LaTex expression showing y=(x+1) to the power of 2 +2
d A LaTex expression showing y=(x-1) to the power of 2 +2
8
Solve the square polynomial to finish factoring
A LaTex expression showing y=(x to the power of 2 +2x+1)-1-1
a A LaTex expression showing y=-1(x-1) to the power of 2 -2
b A LaTex expression showing y=-1(x+1) to the power of 2 -2
c A LaTex expression showing y=(x-1) to the power of 2 +2
d A LaTex expression showing y=(x+1) to the power of 2 -2