Complete the Square/Vertex Form Practice
Teacher Instructions/Information:
This resource is meant to supplement lessons on completing the square (quadratic equations) in order to find the vertex of a quadratic function and write the function in vertex form. The practice problems provide scaffolding to allow students to slowly build up to fully using the process of completing the square.
These problems may be used in your LMS or printed out for students to work on paper. Page breaks and opportunities for students to check in with the teacher are included so that students may show understanding of each step in completing the square and then gradually build on the prior steps to eventually rewrite several equations from standard form to vertex form. Lastly, students will use the vertex form of the equation to identify the vertex of the given equation.
Timeline: 60-120 minutes
Name_____________________
Find k
For each of the following, find the missing term using
.
1. -x2 + 2x +_____  | 2. x2 - 4x+_____  | 3. x2 +8x_____  |
4. x2 - 8x_____  | 5. x2 - 6x_____  | 6. x2 + 18x_____  |
7. x2 + 4x_____  | 8. x2 - 2x_____  | 9. x2 + 10x_____  |
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Name______________________
Factor Perfect Squares
Factor the following. Show work.
| 1. x2 + 6x + 9 | 2. X2 - 8x + 16 |
| 3. x2 - 16x + 64 | 4. x2 + 20x + 100 |
Name_____________________
Finish Completing the Square
Nicole is trying to put the following in questions in vertex form. She started the process but cannot remember the next steps. Help her to finish and put the equations in vertex form.
| 1.y = -x2 + 2x - 2 y = x2 - 2x + 2 -2 -2y - 2 = x2 -2x +1 +1y = ________________ | 2. y = x2 - 4x +4 +4y = ________________ | 3. y = x2 +8x + 18 -18 -18y - 18 = x2 + 8x +16 +16y = ________________ |
| 4. y = x2 - 8x + 15 -15 -15y - 15 = x2 + 8x +16 +16y = ________________ | 5. y = 2x2 - 8x + 6 y = 2x2 - 8x + 6 2y/2 = x2 - 4x + 3 -3 -3 y/2 - 3 = x2 - 4x +4 +4y = ________________ | 6. y = x2 + 18x +81 +81y + 81 = x2 + 18x + 81y = ________________ |
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Name_________________________
Write Factored Form
Write the following equations in factored form and list the x-intercepts.
| 1. y = x2 + 3x - 18 | 2. y = 4x2 - 39x + 27 |
| 3. y = -9x2 + 80x - 64 | 4. y = 2x2 - 4x - 126 |
Name_____________________
Vertex Form & Factored Form Checklist
Have your teacher check off each assignment as you finish. STAPLE COMPLETED WORK!
| Teacher Approval | Assignment Name |
| Find k | |
| Factor Perfect Squares | |
| Finish Completing the Square | |
| Write Factored Form | |
| Converting Quadratic Equations Worksheet | |
| Staple completed worksheets to this form. |
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Name_____________________
Vertex Form & Factored Form Checklist
Have your teacher check off each assignment as you finish. STAPLE COMPLETED WORK!
| Teacher Approval | Assignment Name |
| Find k | |
| Factor Perfect Squares | |
| Finish Completing the Square | |
| Write Factored Form | |
| Converting Quadratic Equations Worksheet | |
| Staple completed worksheets to this form. |
Nicole Smith, 2019 CC, BY