Algebra 2
Algebra 2
1st Edition
ISBN: 9780078884825
Author: McGraw-Hill/Glencoe
Publisher: Glencoe/McGraw-Hill School Pub 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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Question
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Chapter 10, Problem 28SGR
To determine

To find: Theequation of the parabola that models the flight of the football.

Expert Solution & Answer
Check Mark

Answer to Problem 28SGR

The equation of parabola is y =125(x−50)2+100  .

Explanation of Solution

Given information:

A football is thrown from ground level. It reaches a maximum height of 50 feet and hits the ground 200 feet from where it was thrown.

Calculation:

A football is thrown from ground level. It reaches a maximum height of 50 feet and hits the ground 200 feet from where it was thrown. The path of the football is a parabola such that the football was kicked at the origin.

The parabola is of the form y =a(x−h)2 +k . The point of maximum height (A) will be the vertexof the parabola.

  Algebra 2, Chapter 10, Problem 28SGR

The horizontal distance from point O to point A will be half of the distance of OB. So,

  OC = 100 ft

Hence the co-ordinates of vertex A will be

  (h,k)=(50,100)

Substitute h= 50 and k =100 in the standard form y =a(x−h)2 +k the equation of the parabolic path of the baseball will be,

  y =a(x−50)2+100         ..........(1)

Parabola passes through point B. Co-ordinates of point Bare (0,200) Hence

  200=a(0−50)2+100 200 = 2500a + 1002500a=100

  a=125

Substitute a=125 in equation (1) y =a(x−50)2+100  , the equation of the parabola that models the flight of the football will be

  y =125(x−50)2+100 

Therefore, the equation of parabola is y =125(x−50)2+100  .

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Chapter 10, Problem 27SGR
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Chapter 10, Problem 29SGR

Chapter 10 Solutions

Algebra 2

Ch. 10.1 - Prob. 1ACYPCh. 10.1 - Prob. 1BCYPCh. 10.1 - Prob. 2CYPCh. 10.1 - Prob. 3CYPCh. 10.1 - Prob. 1CYUCh. 10.1 - Prob. 2CYUCh. 10.1 - Prob. 3CYUCh. 10.1 - Prob. 4CYUCh. 10.1 - Prob. 5CYUCh. 10.1 - Prob. 6CYU
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