Quadratic Equations: Modelling and Applications
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Quadratic Equations: Modelling and Applications — Free MYP4 Mathematics (Extended) Practice Questions

1QuestionSolving by FactorizationConcept Practice
2 marks~3 minCriterion D
In a soccer match, a player kicks a ball from ground level. Its height, hh metres, after tt seconds is modelled by

h=−5t2+20t.h = -5t^2 + 20t.
a
Factorise −5t2+20t-5t^2 + 20t and hence deduce the time at which the ball returns to the ground. [1]
b
A second player claims the same model applies to her kick, but that her ball stays in the air for 5 seconds. Deduce whether this is possible, and justify your answer using the structure of the factorised expression. [1]
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Solutions

2QuestionPractice Quadratic Equations solvingAssessment Practice
4 marks~6 minCriterion A
A ball is launched upward from a platform. Its height hh (in metres) at time tt (in seconds) is modelled by

h(t)=−5t2+20t+1h(t) = -5t^2 + 20t + 1

The graph of h(t)h(t) has vertex (2, 21)(2,\ 21) and positive tt-intercept at approximately (4.05, 0)(4.05,\ 0).
a
State the initial height of the ball and explain what the coefficient −5-5 indicates about the shape of the graph. [1]
b
Use the quadratic formula to determine the time at which the ball hits the ground. [2]
c
A safety barrier is positioned 20 m above the launch platform. Justify whether the ball clears the barrier. [1]
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Solutions

3QuestionPractice Quadratic Equations solvingAssessment Practice
6 marks~9 minCriterion C
A basketball player shoots a free throw. The height hh (in metres) of the ball tt seconds after release is modelled by

h(t)=−5t2+6t+2.2h(t) = -5t^2 + 6t + 2.2

The basket is at a height of 3.053.05 m above the floor.
a
Calculate the maximum height reached by the ball. [2]
b
Determine the two values of tt at which the ball is at the height of the basket. [2]
c
The ball passes through the basket height twice. Justify which value of tt represents the ball passing through the basket. [2]
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Solutions

4QuestionPractice Quadratic Equations solvingAssessment Practice
5 marks~8 minCriterion B
A projectile is launched from a raised platform. Its height hh (in metres) above the ground is recorded at selected times tt (in seconds):

tt (s)01234
hh (m)1025302510
a
Deduce the quadratic function h(t)=at2+bt+ch(t) = at^2 + bt + c that models the height of the projectile. [2]
b
Determine the maximum height reached by the projectile. [1]
c
The projectile is considered safe to retrieve only if it lands more than 4.0 s after launch. Using your quadratic model, calculate the time at which the projectile hits the ground, then justify whether the retrieval condition is met. [2]

Solutions

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