Graphing Quadratic Cubic and Exponential Functions

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Graphing Quadratic Cubic and Exponential Functions — Free MYP4 Mathematics (Standard) Practice Questions

1QuestionGraphing Simple Cubic FunctionsConcept Practice

2 marks~3 minCriterion A

An engineer models the vibration of a bridge cable using the cubic function

y = x^3 - 2x

, where

x

represents time (seconds) and

y

represents displacement (metres) from equilibrium. The graph of this function is shown below.

State the number of

x

-intercepts of the graph and the coordinates of the

y

-intercept. [2]

Solutions

2QuestionSketching y = ax2 + bx + cAssessment Practice

6 marks~9 minCriterion C

The graph below shows a quadratic function. The vertex is at (2, -1) and the y-intercept is at (0, 3). The x-intercepts are at (1, 0) and (3, 0). Explain, step-by-step, how to determine the equation of the quadratic function in the form

y = ax^2 + bx + c

from the information given in the graph. Justify each step, showing your reasoning clearly using algebraic notation.

Solutions

3QuestionSketching y = ax2 + bx + cConcept Practice

4 marks~6 minCriterion B

Consider the three quadratic functions below, along with their corresponding graphs:

$y = x^2 - 4x + 1$ (Graph A)

y = x^2 - 4x + 4

(Graph B)
*

y = x^2 - 4x - 2

(Graph C)

Investigate the relationship between the constant term in each equation and the

y

-intercept of its graph. Describe the pattern you observe.

Investigate the relationship between the constant term in each equation and the

y

-coordinate of the vertex of the parabola. Describe the pattern you observe.

Generalize a rule for how changing the constant term

c

in the quadratic function

y = ax^2 + bx + c

affects the vertical position of the graph.

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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