Complete the square

Error

There was an error loading the page.

Contributors

Newcastle University Mathematics and Statistics

History

○

Newcastle University Mathematics and Statistics 9 years, 2 months ago

Created this.

There is only one version of this question that you have access to.

There is one other version that you do not have access to.

Question statement

Put the following quadratic expression in the form $a(x+B)^2+C$ for suitable numbers $a$ , $B$ and $C$ .

Note that you have to input your answer in the form $a(x+B)^2+C$ and the numbers $a, \;B,\;C$ must be input exactly (as integers, fractions or exact decimals).

Give any introductory information the student needs.

			Name	Type	Generated Value

a	number	4
s1	integer	1
b	number	-42
k	integer	3

Automatically regenerate variables?

Name

Data type

Value

xxxxxxxxxx
 
s1*random(1.0..4.5#0.5)

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: `number`

← Depends on:

This variable doesn't seem to be used anywhere.

Parts

Gap-fill
1. Gap Mathematical expression
  Add
1. Step Information only

Gap-fill

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

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

Advice

Given the quadratic $q(x)=\simplify{{k}x^2+{2*a*k}x+ {a^2*k+b}}$ we complete the square by:

1. Considering first $\simplify{{k}x^2+{2*a*k}x}$ , taking out the factor $\var{k}$ so that we get $\var{k}(\simplify{x^2+{2*a}x})$ , and complete the square for $\simplify{x^2+{2*a}x}$ .

2. Comparing $\simplify{x^2+{2*a}x}$ to $(x+B)^2=x^2+2Bx+B^2$ : both start with $x^2$ and we set $2B=\var{2*a}$ , so $B=\var{a}$ . Thus $\simplify{(x+{a})^2=x^2+{2*a}x+{a}^2}$ and $\simplify{x^2+{2*a}x=(x+{a})^2-{a}^2}$ .

3. It follows that $\simplify{{k}x^2+{2*a*k}x ={k}((x+{a})^2-{a}^2)={k}(x+{a})^2-{a^2 *k}}$ .

4. Therefore $\simplify{{k}x^2+{2*a*k}x+ {a^2*k+b}={k}(x+{a})^2 +{b}}$ .

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

This question is used in the following exams:

David's copy of Foundation mathematics by David Rickard in David's workspace.
Foundation mathematics by Newcastle University Mathematics and Statistics in Content created by Newcastle University.
week2 by haifa abd in NEM1001.
week3 by haifa abd in NEM1001.
week4 by haifa abd in NEM1001.
week5 by haifa abd in NEM1001.
Foundation mathematics quiz by Simon Thomas in Foundation mathematics.
Maria's copy of Foundation mathematics by Maria Aneiros in Maria's workspace.
Ann's copy of Foundation mathematics by Ann Smith in Foundation Maths.
Ben's copy of Foundation mathematics by Ben Sathuluri in Ben's workspace.
Foundation of Maths by Chris Templet in Chris's workspace.
Robert's copy of Foundation mathematics by Robert Barham in Robert's workspace.
claire's copy of Foundation mathematics by claire lines in claire's workspace.
WeekX-factorise-a-quadratic--from-NCL-algebra by Natalia Martsinovich in Natalia's workspace.
Gesamt-Exam Klasse 11 by Chris Templet in Chris's workspace.

Loading...

Error

Metadata

Taxonomy: mathcentre

Taxonomy: Kind of activity

Taxonomy: Context

Contributors

History

Comment

Checkpoint description

Newcastle University Mathematics and Statistics 9 years, 2 months ago

Error in variable testing condition

Error

Warning

Generated value: `number`

Parts

Gap-fill

Loading...

Error

Complete the square

Metadata

Taxonomy: mathcentre

Taxonomy: Kind of activity

Taxonomy: Context

Contributors

History

Comment

Checkpoint description

Newcastle University Mathematics and Statistics 9 years, 2 months ago

Error in variable testing condition

Error

Warning

Generated value: number

Parts

Gap-fill

Generated value: `number`