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 ) = − 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 .

HARD

Diploma

IMPORTANT

Earn 100

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.

Important Questions on Modelling Relationships: Linear and Quadratic Functions

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.

EASY

Diploma

IMPORTANT

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

Write down the equation of the axis of symmetry and the coordinates of vertex for the graph of function:

$f (x) = 2 (x - 3)^{2} + 4$

EASY

Diploma

IMPORTANT

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

Write down the equation of the axis of symmetry and the coordinates of vertex for the graph of function:

$f (x) = (x - 1)^{2} - 5$

EASY

Diploma

IMPORTANT

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

Write down the equation of the axis of symmetry and the coordinates of vertex for the graph of function:

$f (x) = - 4 (x + 3)^{2} + 2$

EASY

Diploma

IMPORTANT

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

Write down the equation of the axis of symmetry and the coordinates of vertex for the graph of function:

$f (x) = 3 (x + 6)^{2} - 5$

EASY

Diploma

IMPORTANT

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

Find the coordinates of the $y$ -intercept, the equation of the axis of symmetry and the coordinates of the vertex for the graph of function:

$f (x) = x^{2} - 8 x + 5$

EASY

Diploma

IMPORTANT

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

Find the coordinates of the $y$ -intercept, the equation of the axis of symmetry and the coordinates of the vertex for the graph of function:

$f (x) = 3 x^{2} - 6 x + 2$

EASY

Diploma

IMPORTANT

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

Find the coordinates of the $y$ -intercept, the equation of the axis of symmetry and the coordinates of the vertex for the graph of function:

$f (x) = - 2 x^{2} - 8 x - 11$

Sketch the graph of the quadratic function f(x)=−3.6x2+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.

Important Questions on Modelling Relationships: Linear and Quadratic Functions

Learn and Prepare for any exam you want !

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.