Explanation Given information: The quadratic function is f ( x ) = − x 2 − 4 x + 4 . Calculation: The quadratic function f ( x ) = − x 2 − 4 x + 4 is a 2 degree function in x. The quadratic function f ( x ) = a x 2 + b x + c can also be written as, f ( x ) = a x 2 + b x + c = a ( x 2 + b a x + c a ) = a ( x 2 + b a x + b 2 4 a 2 − b 2 4 a 2 + c a ) = a ( x 2 + b a x + b 2 4 a 2 ) − b 2 4 a + c Further solving the quadratic function becomes, f ( x ) = a ( x + b 2 a ) 2 − b 2 − 4 a c 4 a To determine (b) To calculate: The coordinates of the vertex and the x -intercept, y -intercept. To determine (c) To graph: The function f ( x ) = − x 2 − 4 x + 4 . To determine (d) To calculate: The domain and range of the quadratic function.

7th Edition

ISBN: 9781305115545

Author: James Stewart, Lothar Redlin, Saleem Watson

Publisher: Cengage Learning

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Chapter 3.1, Problem 18E

To determine

(a)

To find:

The quadratic function f(x)=ax2+bx+c in standard form.

To determine

(b)

To calculate:

The coordinates of the vertex and the x -intercept, y -intercept.

To determine

(c)

To graph:

The function f(x)=−x2−4x+4.

To determine

(d)

To calculate:

The domain and range of the quadratic function.

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Chapter 3.1, Problem 17E

Chapter 3.1, Problem 19E

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Chapter 3 Solutions

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(a) To find: The quadratic function f ( x ) = a x 2 + b x + c in standard form.

Solution Summary: The author explains that the quadratic function is f(x)=ax 2+bx+c, which is a 2 degree function in x.

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(a)

To find:

The quadratic function f(x)=ax2+bx+c in standard form.

(b)

To calculate:

The coordinates of the vertex and the x -intercept, y -intercept.

(c)

To graph:

The function f(x)=−x2−4x+4.

(d)

To calculate:

The domain and range of the quadratic function.

Want to see the full answer?

Chapter 3 Solutions

(a) To find: The quadratic function f ( x ) = a x 2 + b x + c in standard form.

Solution Summary: The author explains that the quadratic function is f(x)=ax 2+bx+c, which is a 2 degree function in x.

Concept explainers

Videos

(a) To find: The quadratic function f(x)=ax2+bx+c in standard form.

(b) To calculate: The coordinates of the vertex and the x -intercept, y -intercept.

(c) To graph: The function f(x)=−x2−4x+4.

(d) To calculate: The domain and range of the quadratic function.

Want to see the full answer?

Chapter 3 Solutions

(a)

To find:

The quadratic function f(x)=ax2+bx+c in standard form.

(b)

To calculate:

The coordinates of the vertex and the x -intercept, y -intercept.

(c)

To graph:

The function f(x)=−x2−4x+4.

(d)

To calculate:

The domain and range of the quadratic function.