Sketch the graph of the quadratic function f ( x ) = − 3.6 x 2 + 8.1 over the domain − 1.5 ≤ x ≤ 1.5 , labelling the coordinates of key features of the graph. Then write down the range of the function.

We have, f ( x ) = − 3.6 x 2 + 8.1 Here, coefficient of x 2 = - 3 . 6 < 0 ⇒ the parabola will open in downwards direction. Now, making table for f x by taking different values of x . x - 2 - 1 0 1 2 f x - 6 . 3 4 . 5 8 . 1 4 . 5 - 6 . 3 Now, we will plot the graph. From graph, we can make the following observations. x - intercept: ( − 1.5 , 0 ) , ( 1.5 , 0 ) y - intercept: 0 , 8 . 1 . Vertex: ( 0 , 8 . 1 ) . Range of a function f is { y ∈ R ∣ 0 ≤ y ≤ 8 . 1 } because domain of a function is − 1.5 ≤ x ≤ 1.5 and f - 1 . 5 = 0 = f 1 . 5 .

Sketch the graph of the quadratic function , f ( x ) = x 2 − 2 x − 5 , for − 2 ≤ x ≤ 4 labelling the coordinates of key features of the graph. Then write down the range of the function.

We have, undefined Here, coefficient of x 2 = 1 > 0 ⇒ the parabola will open in upwards direction. Now, making table for f x by taking different values of x . x - 2 - 1 0 1 2 f x 3 - 2 - 5 - 6 - 5 Now, we will plot the graph. From graph, we can make the following observations. x - intercept: ( − 1.499 , 0 ) , ( 3 . 449 , 0 ) y - intercept: 0 , - 5 . Vertex: ( 1 , - 6 ) . Range of a function f is { y ∈ R ∣ - 6 ≤ y ≤ 3 } because domain of a function is − 2 ≤ x ≤ 4 and f - 2 = 3 = f 4 .

E M B I B E

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

Natasha Awada, Paul La Rondie, Laurie Buchanan and, Jill Stevens Solutions for Chapter: Modelling Relationships: Linear and Quadratic Functions, Exercise 30: Exercise 3L

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 30: Exercise 3L

Attempt the free practice questions on Chapter 3: Modelling Relationships: Linear and Quadratic Functions, Exercise 30: Exercise 3L 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 30: Exercise 3L with Hints & Solutions

MEDIUM

Diploma

IMPORTANT

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

Sketch the graph of the quadratic function $f (x) = 3 x^{2} + 7 x - 4$ . Use this graph to find the coordinates of the $x -$ intercept, $y -$ intercept and the vertex of the graph.

MEDIUM

Diploma

IMPORTANT

Mathematics : Analysis and Approaches Standard Level Course Companion>Chapter 3 - Modelling Relationships: Linear and Quadratic Functions>Exercise 3L>Q 2

Sketch the graph of the quadratic function $f (x) = - 4.2 x^{2} + 6.1 x - 3$ . Use this graph to find the coordinates of the $x -$ intercept, $y -$ intercept and the vertex of the graph.

HARD

Diploma

IMPORTANT

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

Sketch the graph of the quadratic function $f (x) = - 2 x^{2} - 7 x + 3$ , labelling the coordinates of key features of the graph. Then write down the domain and range of function.

HARD

Diploma

IMPORTANT

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

Sketch the graph of the quadratic function $f (x) = 1.25 x^{2} - 12.4 x$ , labelling the coordinates of key features of the graph. Then write down the domain and range of function.

HARD

Diploma

IMPORTANT

Mathematics : Analysis and Approaches Standard Level Course Companion>Chapter 3 - Modelling Relationships: Linear and Quadratic Functions>Exercise 3L>Q 5

Sketch the graph of the quadratic function $f (x) = - 3.6 x^{2} + 8.1$ over the domain $- 1.5 \leq x \leq 1.5$ , labelling the coordinates of key features of the graph. Then write down the range of the function.

HARD

Diploma

IMPORTANT

Mathematics : Analysis and Approaches Standard Level Course Companion>Chapter 3 - Modelling Relationships: Linear and Quadratic Functions>Exercise 3L>Q 6

Sketch the graph of the quadratic function , $f (x) = x^{2} - 2 x - 5, for - 2 \leq x \leq 4$ labelling the coordinates of key features of the graph. Then write down the range of the function.

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