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Details for problem "Quadratic formula: Complete square to solve equation"

Quickname: 2057

Suitable for K-12 grades: Grade 9 Grade 10

Junior High School, High School, Senior High School.

Summary

To solve a quadratic equation, complete the square.

Examples

To solve a quadratic equation,  complete the square. (Beispiel für die Lösung) To solve a quadratic equation,  complete the square. (Example for this math problem) To solve a quadratic equation,  complete the square. (Example for this math problem)

Description

The solution set of a quadratic equation is to be determined. For this purpose the technique of completing the square is used.

If desired, the solution is described in the solution sheet in the steps

- Convert to monic form

- Complete the square

- Combine like terms on right side

- Introduce square

- Extract root

- Specify the solution set

is presented in detail. These steps can be presented in the problem definition as cloze text, the correct values must then be inserted.

In the problem definition the solution of a quadratic function is asked for. It can be set whether the way of solution via square completion should also be mentioned.

To simplify or complicate the problem, the degree of normalization can be changed. Thus it can be set whether the absolute element should be present (i.e. not equal to zero) or not, and whether the leading coefficient (of x^2) is equal to one or not. In the latter case, coversion to monic form requires a division of the whole equation by the lead coefficient's value.

The number of problems is also adjustable.


Topics: Analysis Functions

Tags: Polynom Quadratic functions Terms

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Customization options for this problem

Parameter
Possible values
Number of problems
1, 2, 3, 4, 5, 6
Mention completion of square
Yes, No
Indicate steps
no, with solution, with problem&solution
Lead coefficient (x^2) >1
Never, May, Always
Absolute value present
Never, May, Always

Similar problems

Remark
Description
Name and direct link
Complete the square to determine the vertex
To determine the vertex of a square function, convert it to vertex form by completing the square.


Creative Commons License
You may pass on the worksheets offered for download on this page to others, but not modify or sell them.
This work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.


Deutsche Version dieser Aufgabe
These informational pages with samples describe math problems that can be combined on custom math worksheets with solutions for home and K-12 school use.
Please visit the dw math main page for more information!
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