EBK PRECALCULUS W/LIMITS
EBK PRECALCULUS W/LIMITS
4th Edition
ISBN: 9781337516853
Author: Larson
Publisher: CENGAGE CO
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Chapter 2.1, Problem 32E
To determine

Tograph: Graph the quadratic function f(x)=−4x2+24x−41 and identify vertex, axis of symmetry and x-intercepts.

Expert Solution & Answer
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Explanation of Solution

Given information: we have the given quadratic function is f(x)=−4x2+24x−41

Graph:

Using graphing calculator, the graph of the function is shown below

  EBK PRECALCULUS W/LIMITS, Chapter 2.1, Problem 32E

Interpretation:

We know that the standard for of a quadratic function f(x)=a(x−h)2+k,  a≠0 whose axis of symmetry is x=h and vertex (h,k) .

For, the above form if a>0 then the graph is open upward and when a<0 the graph is open downward.

We have the given function is f(x)=−4x2+24x−41

It can further written as

  f(x)=−4x2+24x−41=−4(x2−6x+414)=−4{(x−3)2+54}=−4(x−3)2−5

Comparing with above we get

  a=−4<0h=3k=−5

Therefore, the vertex of the parabola is (3,−5) axis of symmetry is x=3 and the graph is open downward.

To get the x-intercept we put f(x)=0 and solve for x which gives

  −4x2+24x−41=0x=3±5i2

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Chapter 2.1, Problem 31E
Next
Chapter 2.1, Problem 33E

Chapter 2 Solutions

EBK PRECALCULUS W/LIMITS

Ch. 2.1 - Prob. 1ECh. 2.1 - Prob. 2ECh. 2.1 - Prob. 3ECh. 2.1 - Prob. 4ECh. 2.1 - Prob. 5ECh. 2.1 - Prob. 6ECh. 2.1 - Prob. 7ECh. 2.1 - Prob. 8ECh. 2.1 - Prob. 9ECh. 2.1 - Prob. 10E
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ISBN:9780134438986
Author:Joel R. Hass, Christopher E. Heil, Maurice D. Weir
Publisher:PEARSON
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ISBN:9780134763644
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Calculus: Early Transcendentals
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Author:Michael Sullivan
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ISBN:9781337552516
Author:Ron Larson, Bruce H. Edwards
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