VOORBEELDOPLOSSING: Vind constante c voor kwadratische functie (gegeven a en b)

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Alexander Holvoet 9 months, 3 weeks ago

Published this.

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Alexander Holvoet 9 months, 3 weeks ago

Created this as a copy of 4 - Find c for quadratic function with given extremal value (a and b given) - full randomisation, different parametrisation.

Name	Status	Author	Last Modified
BASIS: Vind constante c voor kwadratische functie (gegeven a en b)	draft	Alexander Holvoet	02/06/2024 14:35
VOORBEELDOPLOSSING: Vind constante c voor kwadratische functie (gegeven a en b)	draft	Alexander Holvoet	02/06/2024 14:37
Feedback: verschillende opties	draft	Alexander Holvoet	02/06/2024 14:33

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Question statement

The function $f: y=\simplify{{a}*x^2+{b}*x+c}$ has $\var{yv}$ as an extreme value.

Give any introductory information the student needs.

			Name	Type	Generated Value

xv	integer	-5
yv	number	1.4
a	integer	5
b	integer	50
c	number	126.4

Automatically regenerate variables?

Name

Data type

Value

A random number between and (inclusive) with step size

Description

x-coordinate of the vertex

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

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Generated value: `integer`

-5

→ Used by:

Parts

Gap-fill
1. Gap Number entry
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Gap-fill

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

Find $c$ .

$c=$ Unnamed gap

Advice

A quadratic function $f:y=ax^2+bx+c$ has a parabolic graph and reaches it extremal value at the vertex.

The $x$ -value of the vertex is found as $x=-\frac{b}{2a}=\simplify{{-b}/{2*a}}=\var{xv}$ .

The extremal value itself is given by $f(\var{xv})=\var{yv-c}+c$ . Since this must be equal to $\var{yv}$ , we find $\var{yv-c}+c=\var{yv}$ , hence $c=\var{c}$ .

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VOORBEELDOPLOSSING: Vind constante c voor kwadratische functie (gegeven a en b)

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Taxonomy: mathcentre

Taxonomy: Kind of activity

Taxonomy: Context

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Checkpoint description

Alexander Holvoet 9 months, 3 weeks ago

Alexander Holvoet 9 months, 3 weeks ago

Error in variable testing condition

Error

Warning

Generated value: `integer`

Parts

Gap-fill

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Error

VOORBEELDOPLOSSING: Vind constante c voor kwadratische functie (gegeven a en b)

Metadata

Taxonomy: mathcentre

Taxonomy: Kind of activity

Taxonomy: Context

Contributors

History

Comment

Checkpoint description

Alexander Holvoet 9 months, 3 weeks ago

Alexander Holvoet 9 months, 3 weeks ago

Error in variable testing condition

Error

Warning

Generated value: integer

Parts

Gap-fill

Generated value: `integer`