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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Chapter 3.5, Problem 25HP
To determine

To calculate: The values of a, b and c for equation of parabola y=ax2+bx+c if three points (2,−10),(−5,−101),(6,−90) lie on parabola.

Expert Solution & Answer
Check Mark

Answer to Problem 25HP

The equation of parabola is y=−3x2+4x−6.

Explanation of Solution

Given information:

The three points that lie on parabola are (2,−10),(−5,−101),(6,−90).

Calculation:

Consider the three points that lie on parabola are (2,−10),(−5,−101),(6,−90) . The standard form of equation of parabola is y=ax2+bx+c.

Form the system of equations with help of three points.

  a(2)2+b(2)+c=−10a(−5)2+b(−5)+c=−101a(6)2+b(6)+c=−90

Simplify it,

  4a+2b+c=−1025a−5b+c=−10136a+6b+c=−90

Take the first and the second equation,

  4a+2b+c=−1025a−5b+c=−101

Use the method of elimination to solve the system above.

Subtract both the equations,

  4a+2b+c=−1025a−5b+c=−101−−21a+7b=91

Simplify it further as,

  −21a+7b=91−3a+b=13

Take the first and the third equation,

  4a+2b+c=−1036a+6b+c=−90

Multiply first equation by 2.

Use the method of elimination to solve the system above.

Subtract both the equations,

  32a+4b=−808a+b=−20

Solve the system of equation −3a+b=13 and 8a+b=−20.

Subtract both the equations,

  −11a=33a=−3

Substitute a=−3 in the equation −3a+b=13.

  9+b=13b=4

Now substitute a=−3 and b=4 in the equation 4a+2b+c=−10 ,

  −12+8+c=−10c=−10+4c=−6

Now, substitute the values of a, b and c in y=ax2+bx+c.

  y=−3x2+4x−6

Thus, the equation of parabola is y=−3x2+4x−6.

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Chapter 3.5, Problem 24HP
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Chapter 3.5, Problem 26HP

Chapter 3 Solutions

Algebra 2

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