Completing the Square

Error

There was an error loading the page.

Contributors

Feedback

From users who are members of Introduction to Calculus :

Wan Mekwi

said

Ready to use

4 years, 7 months ago

History

○

Wan Mekwi 4 years, 7 months ago

Published this.

○

Wan Mekwi 4 years, 7 months ago

Gave some feedback: Ready to use

○

Wan Mekwi 4 years, 7 months ago

Gave some feedback: Needs to be tested

○

Wan Mekwi 4 years, 7 months ago

Gave some feedback: Has some problems

○

Wan Mekwi 4 years, 7 months ago

Gave some feedback: Needs to be tested

○

Wan Mekwi 4 years, 7 months ago

Created this as a copy of Factorising Quadratics 5 - Completing the Square.

Name	Status	Author	Last Modified
Complete the square	draft	Bill Foster	06/08/2020 08:29
Factorising Quadratics 5 - Completing the Square	Ready to use	Katie Lester	01/06/2016 09:47
Lois's copy of Complete the square	draft	Lois Rollings	25/10/2017 10:26
My Completing the Square	draft	steve kilgallon	05/09/2016 16:13
Completing the Square	Ready to use	Wan Mekwi	17/09/2021 10:28

There are 24 other versions that do you not have access to.

Question statement

Rewrite the expression

$\simplify{{a}x^2+{b}x+{c}}$ in completed square form

$a(x+k)^2+p$ for suitable numbers

$a, k$ and

$p$ .

Your answer must be input exactly in this form.

Give any introductory information the student needs.

			Name	Type	Generated Value

a	integer	-4
c	integer	13
b	integer	7

Automatically regenerate variables?

Name

Data type

Value

xxxxxxxxxx
 
random(-5..7 except 0)

JME function reference

Description

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

Can an exam override the value of this variable?

Generated value: `integer`

-4

This variable doesn't seem to be used anywhere.

Parts

(a) Gap-fill
1. Gap Mathematical expression
  Add
1. Step Information only
(b) Gap-fill
1. Gap Matrix entry
  Add
1. Step Information only

Gap-fill

Ask the student a question, and give any hints about how they should answer this part.

$\simplify{{a}x^2+{b}x+ {c}} = \phantom{{}}$ Unnamed gap.

Advice

(a)

Given the quadratic $q(x)=\simplify{{a}x^2+{b}x+ {c}}$ , one way of completing the square is to simply expand the term $a(x+k)^2+p$ and equate coefficients to the quadratic term.

Expanding $a(x+k)^2+p$ gives $ax^2 + 2akx + ak^2 + p$ .

Equating coefficients gives:

$x^2:\quad \var{a}=a$ or $a=\var{a}$ .

$x:\quad \var{b}= 2ak \implies k = \simplify{{b}/(2{a})}$

constant: $\var{c}=ak^2+p \implies p=\var{c}-ak^2=\simplify[all, fractionNumbers]{{c-b^2/(4a)}}$ .

Now, put these together to obtain: $\qquad \simplify[all, fractionNumbers]{{a}(x+{b}/(2{a}))^2+{c-b^2/(4a)}}$ .

(b)

Completing the square for this function gives: $\qquad \simplify[all, fractionNumbers]{{a}(x+{b}/(2{a}))^2+{c-b^2/(4a)}}$ .

The function attains its turning point when $\quad \simplify{{a}(x+{b}/(2{a}))^2}=0$

So the $x$ coordinate of the turning point is $\simplify{-{b}/(2{a})}$ .

The $y$ coordinate is $k=\simplify[all, fractionNumbers]{{c-b^2/(4a)}}$ .

Hence the turning point is $\quad (\simplify{-{b}/(2{a})},\simplify[all, fractionNumbers]{{c-b^2/(4a)}})$

Give a worked solution to the whole question.

Use this tab to check that this question works as expected.

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

Part	Test	Passed?
Gap-fill
Gap-fill		Hasn't run yet
Mathematical expression
Mathematical expression		Hasn't run yet
Information only
Gap-fill
Gap-fill		Hasn't run yet
Matrix entry
Matrix entry		Hasn't run yet
Information only

This question is used in the following exams:

Quadratic expressions and equations by Wan Mekwi in Introduction to Calculus.
Access Maths formative test 1 by Ruth Douglas in Ruth's workspace.
Solving Quadratics by Kevin Bohan in Kevin's workspace.
N5 Math Prelim Trial 2 by Nevil Hopley in Nevil's workspace.
Test Homework by Connor Fenton in Connor's workspace.
Excellent quadratic equations questions and answers by Nahid Chowdhury in FS0031 Unit 3.
EC1602 Exam part1 by samira Al-Moustafa in samira's workspace.
Mock Exam by samira Al-Moustafa in samira's workspace.
EC1602 Numbas 3 by samira Al-Moustafa in samira's workspace.

Loading...

Error

Metadata

Taxonomy: mathcentre

Taxonomy: Kind of activity

Taxonomy: Context

Contributors

Feedback

History

Comment

Checkpoint description

Wan Mekwi 4 years, 7 months ago

Wan Mekwi 4 years, 7 months ago

Wan Mekwi 4 years, 7 months ago

Wan Mekwi 4 years, 7 months ago

Wan Mekwi 4 years, 7 months ago

Wan Mekwi 4 years, 7 months ago

Error in variable testing condition

Error

Warning

Generated value: `integer`

Parts

Gap-fill

Loading...

Error

Completing the Square

Metadata

Taxonomy: mathcentre

Taxonomy: Kind of activity

Taxonomy: Context

Contributors

Feedback

History

Comment

Checkpoint description

Wan Mekwi 4 years, 7 months ago

Wan Mekwi 4 years, 7 months ago

Wan Mekwi 4 years, 7 months ago

Wan Mekwi 4 years, 7 months ago

Wan Mekwi 4 years, 7 months ago

Wan Mekwi 4 years, 7 months ago

Error in variable testing condition

Error

Warning

Generated value: integer

Parts

Gap-fill

Generated value: `integer`