Quadratic Functions 1

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Needs to be tested

4 years, 11 months ago

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Johnathan Gregg 4 years, 11 months ago

Gave some feedback: Needs to be tested

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Johnathan Gregg 4 years, 11 months ago

Published this.

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Johnathan Gregg 4 years, 11 months ago

Gave some feedback: Ready to use

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Johnathan Gregg 4 years, 11 months ago

Gave some feedback: Needs to be tested

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Johnathan Gregg 4 years, 11 months ago

Created this.

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Question statement

Consider the quadratic function, $f(x) = px (q−x)$ , where $p$ and $q$ are positive integers. The graph of $y = f(x)$ passes through the point ({q}, 0).

Give any introductory information the student needs.

			Name	Type	Generated Value

p	integer	2
q	integer	1
ver_x	rational	1/2
ver_y	rational	1/2

Automatically regenerate variables?

Name

Data type

Value

A random number between and (inclusive) with step size

Description

p in equation px(q-x)

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`

This variable doesn't seem to be used anywhere.

Advice

In part (a) note that the factorised form of the equation gives the two vertices. Evaluate when the function is zero.

This occurs at the origin and when $x = q$ . Therefore $q =$ {q}

In part (b) $p$ can be evaluated by substituting the values of $x$ and $y$ at the vertex into the equation.

{ver_y} $= p \times$ {ver_x} $($ {q} $-$ {ver_x} $)$

$p =$ {ver_y} $\div [$ {ver_x} $\times($ {q} $-$ {ver_x} $)]$

$p =$ {p}

In part (c) note that the coefficient of $x^2$ is negative and therefore the parabola is concave down.

The range can be calculated from the y-coordinate of the vertex since this is a maximum point.

$y \leq$ {ver_y}

Give a worked solution to the whole question.

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This question is used in the following exams:

End of Year IB1 Exam HL by Johnathan Gregg in Johnathan's workspace.
End of Year IB1 Exam SL by Johnathan Gregg in Johnathan's workspace.
End of Year Exam by Johnathan Gregg in Johnathan's workspace.

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Taxonomy: mathcentre

Taxonomy: Kind of activity

Taxonomy: Context

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Checkpoint description

Johnathan Gregg 4 years, 11 months ago

Johnathan Gregg 4 years, 11 months ago

Johnathan Gregg 4 years, 11 months ago

Johnathan Gregg 4 years, 11 months ago

Johnathan Gregg 4 years, 11 months ago

Error in variable testing condition

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Warning

Generated value: `integer`

Parts

Number entry

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Quadratic Functions 1

Metadata

Taxonomy: mathcentre

Taxonomy: Kind of activity

Taxonomy: Context

Contributors

Feedback

History

Comment

Checkpoint description

Johnathan Gregg 4 years, 11 months ago

Johnathan Gregg 4 years, 11 months ago

Johnathan Gregg 4 years, 11 months ago

Johnathan Gregg 4 years, 11 months ago

Johnathan Gregg 4 years, 11 months ago

Error in variable testing condition

Error

Warning

Generated value: integer

Parts

Number entry

Advanced settings

Generated value: `integer`