Family of parabolas

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Question statement

{applet}

The equation for a parabola with vertex at the origin is given by the general equation

$y=kx^2$.

This equation describes an infinite family of parabolas, each corresponding to a different value of $k$.

Give any introductory information the student needs.

			Name	Type	Generated Value

applet	ggbapplet	HTML node
k	number	-0.2445356841
A	vector	vector(3.64,-3.24)
h	expression	b
point	list	[ "a", "b" ]
b	expression	a

Automatically regenerate variables?

Name

Data type

Value

xxxxxxxxxx
 
geogebra_applet("nrjjmhuh",[A: A])

JME function reference

This variable is an interactive HTML node. Interactive HTML nodes can not be relied upon to work correctly when resuming a session - for example, attached event callbacks will be lost, and mathematical notation will likely also break.

If this causes problems, try to create HTML nodes where you use them in content areas, instead of storing them in variables.

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: `ggbapplet`

GeoGebra applet loading...

← Depends on:

This variable doesn't seem to be used anywhere.

Parts

Gap-fill
1. Gap Estimate Number entry
  Add
2. Gap exact Number entry
  Add
3. Gap expression Mathematical expression
  Add

Gap-fill

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

Use the slider to find the approximate value of $k$ ($\pm 0.1$) required so that the parabola passes through the indicated point. (You may use the arrow keys for finer adjustment of the slider.)

$k_{est} = $ Estimate

Now substitute the coordinates of the known point into the equation of the parabola and solve for the exact value of $k$ to three significant figures.

$k =$ exact

Determine the equation for a parabola with a vertex at the origin, which passes through a known point located at $(\var{b}, \var{h})$.

$y =$ expression

Advice

Substituting in the known coordnates of the point into the equation of the parabola for $k$ gives:

$k = \dfrac{y}{x^2} = \dfrac{\var{A[1]}}{\var{A[0]}^2} = \var{sigformat(k,3)}$.

The value of $k$ for a parabola passing through the point $(\var{b}, \var{h})$ is determined the same way, and the resulting equation for the parabola is

$y= \dfrac{\var{h}}{\var{b}^2}\; x^2$

Give a worked solution to the whole question.

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

Part	Test	Passed?
Gap-fill
Gap-fill		Hasn't run yet
Number entry
Number entry		Hasn't run yet
Number entry
Number entry		Hasn't run yet
Mathematical expression
Mathematical expression		Hasn't run yet

This question is used in the following exam:

20. Integration Review by William Haynes in Engineering Statics.

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Metadata

Taxonomy: mathcentre

Taxonomy: Kind of activity

Taxonomy: Context

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Checkpoint description

William Haynes 2 years, 4 months ago

William Haynes 2 years, 4 months ago

William Haynes 2 years, 4 months ago

Error in variable testing condition

Error

Warning

Generated value: `ggbapplet`

Parts

Gap-fill

Loading...

Error

Family of parabolas

Metadata

Taxonomy: mathcentre

Taxonomy: Kind of activity

Taxonomy: Context

Contributors

Feedback

History

Comment

Checkpoint description

William Haynes 2 years, 4 months ago

William Haynes 2 years, 4 months ago

William Haynes 2 years, 4 months ago

Error in variable testing condition

Error

Warning

Generated value: ggbapplet

Parts

Gap-fill

Generated value: `ggbapplet`