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.

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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 (Coefficient 1)
1
Solve the square polynomial to finish converting this to vertex form
A LaTex expression showing y=(x to the power of 2 -4x+4)-4+2
a A LaTex expression showing y=-1(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
2
Solve the square polynomial to finish converting this to vertex form
A LaTex expression showing y=(x to the power of 2 -2x+1)-1+4
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=(x-1) to the power of 2 +3
d A LaTex expression showing y=-1(x+1) to the power of 2 +3
3
Solve the square polynomial to finish converting this to vertex form
A LaTex expression showing y=(x to the power of 2 -4x+4)-4+8
a A LaTex expression showing y=(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
4
Solve the square polynomial to finish converting this to vertex form
A LaTex expression showing y=(x to the power of 2 +4x+4)-4+2
a A LaTex expression showing y=(x+2) to the power of 2 -2
b A LaTex expression showing y=-1(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
5
Solve the square polynomial to finish converting this to vertex form
A LaTex expression showing y=(x to the power of 2 -6x+9)-9+10
a A LaTex expression showing y=(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=(x-3) to the power of 2 +1
d A LaTex expression showing y=-1(x-3) to the power of 2 +1
6
Solve the square polynomial to finish converting this to vertex form
A LaTex expression showing y=(x to the power of 2 -8x+16)-16+19
a A LaTex expression showing y=(x+4) to the power of 2 +3
b A LaTex expression showing y=(x-4) to the power of 2 +3
c A LaTex expression showing y=(x-4) to the power of 2 -3
d A LaTex expression showing y=(x+4) to the power of 2 -3
7
Solve the square polynomial to finish converting this to vertex form
A LaTex expression showing y=(x to the power of 2 -6x+9)-9+6
a A LaTex expression showing y=(x-3) to the power of 2 -3
b A LaTex expression showing y=(x+3) to the power of 2 -3
c A LaTex expression showing y=(x-3) to the power of 2 +3
d A LaTex expression showing y=(x+3) to the power of 2 +3
8
Solve the square polynomial to finish converting this to vertex form
A LaTex expression showing y=(x to the power of 2 +8x+16)-16+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=(x-4) to the power of 2 -4
d A LaTex expression showing y=(x+4) to the power of 2 -4