The shape of an archway is modelled by the graph of a quadratic function. The maximum height of the archway is 4 m and the maximum width is 4 m . The graph shows a model of the archway. Find a function to model the archway. Use the function to determine whether an object 3 m wide and 1 . 6 m tall will fit through the archway.

Let x be the horizontal distance from the left side of the arch and let y be the vertical distance above the floor. Then, the required equation will be y = a ( x − h ) 2 + k , where a = - 1 , h = 2 , k = 4 ⇒ y = − ( x − 2 ) 2 + 4 ⇒ y = - x 2 + 4 - 4 x + 4 ⇒ y = - x 2 - 4 + 4 x + 4 ⇒ y = - x 2 + 4 x . If the centre of the object is aligned with the centre of the archway, it spans from x = 0.5 to x = 3.5 . Now, evaluating the function at x = 0 . 5 and at x = 3 . 5 . y = − 0 . 5 2 + 4 0 . 5 = 1 . 75 and y = − 3 . 5 2 + 4 3 . 5 = 1 . 75 . Since, 1.6 < 1.75 , so the object will fit through the archway.

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Mathematics : Analysis and Approaches Standard Level Course Companion>Chapter 3 - Modelling Relationships: Linear and Quadratic Functions>Exercise 3X

Natasha Awada, Paul La Rondie, Laurie Buchanan and, Jill Stevens Solutions for Chapter: Modelling Relationships: Linear and Quadratic Functions, Exercise 64: Exercise 3X

Author:Natasha Awada, Paul La Rondie, Laurie Buchanan & Jill Stevens

Natasha Awada Mathematics Solutions for Exercise - Natasha Awada, Paul La Rondie, Laurie Buchanan and, Jill Stevens Solutions for Chapter: Modelling Relationships: Linear and Quadratic Functions, Exercise 64: Exercise 3X

Attempt the practice questions on Chapter 3: Modelling Relationships: Linear and Quadratic Functions, Exercise 64: Exercise 3X with hints and solutions to strengthen your understanding. Mathematics : Analysis and Approaches Standard Level Course Companion solutions are prepared by Experienced Embibe Experts.

Questions from Natasha Awada, Paul La Rondie, Laurie Buchanan and, Jill Stevens Solutions for Chapter: Modelling Relationships: Linear and Quadratic Functions, Exercise 64: Exercise 3X with Hints & Solutions

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Mathematics : Analysis and Approaches Standard Level Course Companion>Chapter 3 - Modelling Relationships: Linear and Quadratic Functions>Exercise 3X>Q 1

The length of the base of a triangle is four more than twice the height. The area of the triangle is $24 m^{2}$ . Find the lengths of the base and height of the triangle.

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Mathematics : Analysis and Approaches Standard Level Course Companion>Chapter 3 - Modelling Relationships: Linear and Quadratic Functions>Exercise 3X>Q 4

The shape of an archway is modelled by the graph of a quadratic function. The maximum height of the archway is $4 m$ and the maximum width is $4 m$ . The graph shows a model of the archway.

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