Algebra 2
Algebra 2
1st Edition
ISBN: 9780078884825
Author: McGraw-Hill/Glencoe
Publisher: Glencoe/McGraw-Hill School Pub Co
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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+4x6.

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=1025a5b+c=10136a+6b+c=90

Take the first and the second equation,

  4a+2b+c=1025a5b+c=101

Use the method of elimination to solve the system above.

Subtract both the equations,

  4a+2b+c=1025a5b+c=10121a+7b=91

Simplify it further as,

  21a+7b=913a+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+4x6

Thus, the equation of parabola is y=3x2+4x6.

Chapter 3 Solutions

Algebra 2

Ch. 3.1 - Prob. 2CYUCh. 3.1 - Prob. 3CYUCh. 3.1 - Prob. 4CYUCh. 3.1 - Prob. 5CYUCh. 3.1 - Prob. 6CYUCh. 3.1 - Prob. 7CYUCh. 3.1 - Prob. 8CYUCh. 3.1 - Prob. 9CYUCh. 3.1 - Prob. 10CYUCh. 3.1 - Prob. 11CYUCh. 3.1 - Prob. 12CYUCh. 3.1 - Prob. 13PPSCh. 3.1 - Prob. 14PPSCh. 3.1 - Prob. 15PPSCh. 3.1 - Prob. 16PPSCh. 3.1 - Prob. 17PPSCh. 3.1 - Prob. 18PPSCh. 3.1 - Prob. 19PPSCh. 3.1 - Prob. 20PPSCh. 3.1 - Prob. 21PPSCh. 3.1 - Prob. 22PPSCh. 3.1 - Prob. 23PPSCh. 3.1 - Prob. 24PPSCh. 3.1 - Prob. 25PPSCh. 3.1 - Prob. 26PPSCh. 3.1 - Prob. 27PPSCh. 3.1 - Prob. 28PPSCh. 3.1 - Prob. 29PPSCh. 3.1 - Prob. 30PPSCh. 3.1 - Prob. 31PPSCh. 3.1 - Prob. 32PPSCh. 3.1 - Prob. 33PPSCh. 3.1 - Prob. 34PPSCh. 3.1 - Prob. 35PPSCh. 3.1 - Prob. 36PPSCh. 3.1 - Prob. 37PPSCh. 3.1 - Prob. 38PPSCh. 3.1 - Prob. 39PPSCh. 3.1 - Prob. 40PPSCh. 3.1 - Prob. 41PPSCh. 3.1 - Prob. 42HPCh. 3.1 - Prob. 43HPCh. 3.1 - Prob. 44HPCh. 3.1 - Prob. 45HPCh. 3.1 - Prob. 46HPCh. 3.1 - Prob. 47HPCh. 3.1 - Prob. 48HPCh. 3.1 - Prob. 49HPCh. 3.1 - 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