Quadratics: Completing the Square 2

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Ben McGovern

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3 years, 9 months ago

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Ben McGovern 2 years, 7 months ago

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Ben McGovern 3 years, 9 months ago

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Ben McGovern 4 years, 10 months ago

Created this as a copy of Quadratics: Completing the Square 1.

Name	Status	Author	Last Modified
Surds: Simplifying Expressions 1a	Ready to use	Ben McGovern	15/08/2023 15:04
Surds: Simplifying Expressions 1b	Ready to use	Ben McGovern	15/08/2023 15:04
Surds: Simplifying Expressions 2b	Ready to use	Ben McGovern	15/08/2023 15:49
Surds: Simplifying Expressions 2a	Ready to use	Ben McGovern	15/08/2023 15:49
Surds: Simplifying Expressions 3a	Ready to use	Ben McGovern	15/08/2023 15:31
Surds: Simplifying Expressions 3b	Ready to use	Ben McGovern	15/08/2023 15:14
Surds: Simplifying Expressions 4a	Ready to use	Ben McGovern	15/08/2023 15:29
Surds: Simplifying Expressions 4b	Ready to use	Ben McGovern	15/08/2023 15:26
Surds: Simplifying Expressions 4c	Ready to use	Ben McGovern	15/08/2023 15:50
Surds: Simplifying Expressions 5a - Rationalising the Denominator	Ready to use	Ben McGovern	15/08/2023 15:55
Surds: Simplifying Expressions 5b - Rationalising the Denominator	Ready to use	Ben McGovern	15/08/2023 16:07
Surds: Simplifying Expressions 6 - Rationalising the Denominator	Ready to use	Ben McGovern	21/09/2022 16:31
Surds: Simplifying Expressions 7 - Rationalising the Denominator	Ready to use	Ben McGovern	21/09/2022 16:31
Quadratics: Using the Quadratic Formula	Ready to use	Ben McGovern	14/09/2022 16:14
Quadratics: Factorisation 1	Ready to use	Ben McGovern	14/08/2023 15:01
Quadratics: Factorisation 2	Ready to use	Ben McGovern	14/08/2023 15:14
Quadratics: Completing the Square 1	Ready to use	Ben McGovern	14/08/2023 14:59
Quadratics: Completing the Square 2	Ready to use	Ben McGovern	14/09/2022 16:03
Quadratics: Interpreting the Discriminant	Ready to use	Ben McGovern	14/09/2022 16:08
Quadratics: Factorisation 3 - Difference of 2 squares	Ready to use	Ben McGovern	14/08/2023 15:33
Indices: Simplification 1a	Ready to use	Ben McGovern	26/06/2023 12:12
Indices: Simplification 1b	Ready to use	Ben McGovern	26/06/2023 14:31
Indices: Simplification 1c	Ready to use	Ben McGovern	26/06/2023 14:30
Indices: Simplification 2a	Ready to use	Ben McGovern	26/06/2023 14:33
Indices: Simplification 2b	Ready to use	Ben McGovern	26/06/2023 14:36
Indices: Simplification 3a	Ready to use	Ben McGovern	26/06/2023 14:37
Indices: Simplification 3b	Ready to use	Ben McGovern	26/06/2023 14:40
Indices: Change of Notation 1	Ready to use	Ben McGovern	15/08/2023 11:43
Indices: Change of Notation 2	Ready to use	Ben McGovern	15/08/2023 11:51
Indices: Change of Notation 3	Ready to use	Ben McGovern	15/08/2023 11:54
Solve Quadratics - Factorisation 1	Ready to use	Ruth Hand	14/08/2023 15:44
Quadratics: Solving a Quadratic Equation	Ready to use	Ben McGovern	09/12/2022 16:45
Quadratics: Solving by Factorisation	Ready to use	Ben McGovern	14/09/2022 16:25
AD2 Quadratics - solve	Ready to use	Megan Oliver	09/04/2024 15:13
AD5 Difference of two squares	Ready to use	Megan Oliver	09/04/2024 15:14
AA2 Indices - divide	Ready to use	Andrew Neate	09/04/2024 15:00
AA4 Indices - Fractional 2	Ready to use	Andrew Neate	09/04/2024 15:01
AA3 Indices - Fractional 1	Ready to use	Andrew Neate	09/04/2024 15:01
AA1 Indices - times	Ready to use	Andrew Neate	28/03/2024 13:17
Calculation with indices - times	Ready to use	Will Morgan	26/06/2024 11:53
Calculation with Indices - divide	Ready to use	Will Morgan	26/06/2024 12:07

There are 209 other versions that do you not have access to.

Question statement

Write the following quadratic expression in the form $a(x+b)^2+c$ by using the method of completing the square:

$\simplify[unitFactor]{{a}x^2+{b}x+{c}}$

Give any introductory information the student needs.

			Name	Type	Generated Value

a	integer	2
b	integer	-2
c	integer	-20
p	integer	-5
q	integer	4

Automatically regenerate variables?

Name

Data type

Value

xxxxxxxxxx
 
random(2..5)

JME function reference

Description

Describe what this variable represents, and list any assumptions made about its value.

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Generated value: `integer`

→ Used by:

Statement
Advice
"Unnamed part" - Correct answer
"Unnamed part" - Pattern student's answer must match

Advice

For a quadratic expression of the form

$ax^2+bx+c,$ when written in completed square form it becomes

$a\left(x+\frac{b}{2a}\right)^2 - \left(\frac{b^2}{4a}\right)+c.$

So,

$\begin{split} \simplify[unitFactor]{{a}x^2+{b}x+{c}} &\,= \simplify[unitFactor,fractionNumbers]{{a}(x^2+{b/a} x) +{c}} \\ &\,=\simplify[unitFactor,fractionNumbers]{{a}((x+{b/(2a)})^2 - {(b/(2a))}^2) + {c}}, \\ &\,=\simplify[unitFactor,fractionNumbers]{{a}(x+{b/(2a)})^2 - {(b^2/(4a))} + {c}} \\&\,=\simplify[all,fractionNumbers]{{a}(x+{b/(2a)})^2 +{c-(b^2/(4a))}}. \end{split}$

Give a worked solution to the whole question.

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There was an error which means the tests can't run:

Numbas Error: Part a: Variable <code>a</code> is not defined.

Part	Test	Passed?
Mathematical expression
Mathematical expression		Hasn't run yet

This question is used in the following exams:

Quadratic Functions Quiz by Ruth Hand in MASH Bath: Moodle quizzes and TS.
Quadratics by Ben McGovern in MASH Bath: Moodle quizzes and TS.
Week 4 e-quiz by Ruth Douglas in Ruth's workspace.
All about quadratics by Jinhua Mathias in Maths 3-2020.
All the good stuff by Chris Templet in Chris's workspace.

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Ben McGovern 2 years, 7 months ago

Ben McGovern 3 years, 9 months ago

Ben McGovern 4 years, 10 months ago

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Quadratics: Completing the Square 2

Metadata

Taxonomy: mathcentre

Taxonomy: Kind of activity

Taxonomy: Context

Contributors

Feedback

History

Comment

Checkpoint description

Ben McGovern 2 years, 7 months ago

Ben McGovern 3 years, 9 months ago

Ben McGovern 4 years, 10 months ago

Error in variable testing condition

Error

Warning

Generated value: integer

Parts

Mathematical expression

Advanced settings

Checking accuracy

Variable value generators

Pattern restriction

Variables

String restrictions

Generated value: `integer`