Graphing Quadratic Cubic and Exponential Functions

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Graphing Quadratic Cubic and Exponential Functions — Free MYP5 Mathematics (Standard) Practice Questions

1QuestionGraphing Simple Cubic FunctionsConcept Practice

2 marks~3 minCriterion A

An engineer models the vertical displacement of a suspension bridge cable using the cubic function

y = x^3 - 4x

, where

x

is the horizontal distance (in metres) from the centre of the bridge and

y

is the vertical displacement (in metres) from the reference level.

The graph of

y = x^3 - 4x

is provided.

Deduce the

y

-intercept of the graph, showing your working. [1]

Interpret what the

y

-intercept means in the context of the bridge model. [1]

Solutions

2QuestionGraphing and Identifying Exponential Growth and DecayAssessment Practice

4 marks~6 minCriterion D

A wildlife reserve records the population of a rare beetle species over four consecutive years. The population is modelled by an exponential function. The graph shows population

P

(in hundreds) against time

t

(in years), with points

(0, 3)

(1, 6)

(2, 12)

(3, 24)

labelled.

State the initial population and deduce the growth factor from the graph. [2]

Write the equation of the exponential model in the form

P = a \cdot b^t

. [1]

The reserve can sustainably support a maximum of 5000 beetles. Advise the reserve manager whether intervention is required before year

t = 5

, justifying your answer with a calculation. [1]

Solutions

3QuestionSketching y = ax2 + bx + cConcept Practice

4 marks~6 minCriterion B

The graphs of four quadratic functions are shown below. All graphs share the same vertex at (0, 0).

Graph 1:

y = x^2

Graph 2:

y = 3x^2

Graph 3:

y = 0.5x^2

Graph 4:

y = -x^2

Graph	Equation	Opens	Width Compared to $y=x^2$
1	$y = x^2$	Up	Same
2	$y = 3x^2$	Up	Narrower
3	$y = 0.5x^2$	Up	Wider
4	$y = -x^2$	Down	Same

Investigate the relationship between the coefficient of the

x^2

term (the value of 'a' in

y=ax^2

) and the following characteristics of the parabola:
(i) Whether the parabola opens upwards or downwards.
(ii) The width of the parabola compared to

y=x^2

Generalize your findings into rules describing how the value of 'a' affects the graph of the quadratic function.

Predict what the graph of

y = -0.5x^2

would look like. How would its direction and width compare to the other graphs?

Solutions

4QuestionFinding Vertex and Axis of SymmetryAssessment Practice

8 marks~12 minCriterion D

A drone's height above the ground (in metres) is modelled by

h(t) = -5t^2 + 40t + 10

where

t

is the time in seconds after launch.

Determine the time at which the drone reaches its maximum height and calculate that maximum height. [2]

The drone operates safely only when its height is at least 15 m. Deduce the time interval during which the drone maintains a safe height. [2]

A safety regulation states the drone must remain above 15 m for at least 7 seconds. Using your results, advise the drone operator whether this model provides sufficient assurance of compliance with the regulation, and justify your advice by identifying one reason why the real flight may not match the model's prediction. [4]

Solutions

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