Complete the square

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Newcastle University Mathematics and Statistics

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Newcastle University Mathematics and Statistics 9 years, 2 months ago

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Question statement

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

Note that you have to input your answer in the form $(x+B)^2+C$ and the numbers $B,\;C$ must be input exactly (they can be entered as integers, as fractions or as exact decimals). If $C=0$ , then it may be omitted in the answer.

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			Name	Type	Generated Value

a	number	2.5
s1	integer	1
b	number	2.75

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Name

Data type

Value

xxxxxxxxxx
 
s1*random(1.0..4.5#0.5)

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Description

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Generated value: `number`

2.5

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Parts

Gap-fill
1. Gap Mathematical expression
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Gap-fill

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

Advice

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

1. Considering first $\simplify{x^2+{2*a}x}$ and comparing 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 $\simplify{x^2+{2*a}x=(x+{a})^2-{a}^2}$ .

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

3. Hence we get

$q(x) = \simplify[all]{ (x+{a})^2+{b}}$

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Taxonomy: mathcentre

Taxonomy: Kind of activity

Taxonomy: Context

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Newcastle University Mathematics and Statistics 9 years, 2 months ago

Error in variable testing condition

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Generated value: `number`

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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`