EBK PRECALCULUS W/LIMITS
EBK PRECALCULUS W/LIMITS
4th Edition
ISBN: 9781337516853
Author: Larson
Publisher: CENGAGE CO
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Concept explainers

Maximization
Have you ever seen a bridge in the shape of a parabola? Where is its maximum on the bridge? The maximum of that bridge is the highest point on that bridge. The process of finding the maximum of the bridge here is called the maximization.
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Chapter 2.1, Problem 19E
To determine

To write: write the given function f(x)=x2−8x+21 in standard form and find the vertex, axis of symmetry and x-intercept.

Expert Solution & Answer
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Answer to Problem 19E

The vertex of the parabola is (4,5) , axis of symmetry is x=4 and the graph is open upward.

Explanation of Solution

Given information: Given that the quadratic function is f(x)=x2−8x+21

We know that the standard form of parabola is 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)=x2−8x+21

It can further written as

  f(x)=x2−8x+21=(x−4)2+5

Comparing with above we get

  a=1>0h=4k=5

Therefore, the vertex of the parabola is (4,5) axis of symmetry is x=4 and the graph is open upward.

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

  (x−4)2+5=0x=4±5i

The graph of the quadratic function is shown below.

  EBK PRECALCULUS W/LIMITS, Chapter 2.1, Problem 19E

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Chapter 2.1, Problem 20E

Chapter 2 Solutions

EBK PRECALCULUS W/LIMITS

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Finding The Focus and Directrix of a Parabola - Conic Sections; Author: The Organic Chemistry Tutor;https://www.youtube.com/watch?v=KYgmOTLbuqE;License: Standard YouTube License, CC-BY