EBK PRECALCULUS W/LIMITS
4th Edition
ISBN: 9781337516853
Author: Larson
Publisher: CENGAGE CO
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Question
Chapter 7, Problem 20CT
To determine
To find: the equation of the given parabola,that passes through the points (0,6),(−2,2) , and (3,93) .
Expert Solution & Answer
Answer to Problem 20CT
y=−12x2+x+6
Explanation of Solution
Given information:
The given parabola is y=ax2+bx+c ,
Given points are (0.6),(−2,2),(3,92) .
Calculation:
Consider a parabola y=ax2+bx+cwhich passes through the following points
(0.6),(−2,2),(3,92)
Since the points lie on the parabola, therefore each the satisfy the equation of the parabola
Since the point (0.6) satisfy y=ax2+bx+c
6=a(0)2+b(0)+c6=c................(1)
Since the point (−2,2) satisfy y=ax2+bx+c
2=a(−2)2+b(−2)+c2=4a−2b+c..............(2)
Also, the point (3,92) satisfy y=ax2+bx+c
92=a(3)2+b(3)+c92=9a+3b+c..........(3)a
Substitute the value of c from (1) in (2)
2=4a−2b+6−4=4a−2b
Divide both sides by 2
−2=2a−b.........(4)
Substitute the value of c from (1) in (3)
92=9a+3b+6−32=9a+3b
Divide both sides by 3
−12=3a+b.............(5)
Add equations (4) and (5)
−52=5a
Divide both sides by 5
−12=a
Put a=−12in equation (4)
−2=2(−12)−b−2=−1−b
Add 1 to both sides
−1=−b
Multiply both sides by -1
1=b
Put values of a,b,c into y=ax2+bx+cto obtain the equation of parabola
y=−12x2+x+6 .
Chapter 7 Solutions
EBK PRECALCULUS W/LIMITS
Ch. 7.1 - Prob. 1ECh. 7.1 - Prob. 2ECh. 7.1 - Prob. 3ECh. 7.1 - Prob. 4ECh. 7.1 - Prob. 5ECh. 7.1 - Prob. 6ECh. 7.1 - Prob. 7ECh. 7.1 - Prob. 8ECh. 7.1 - Prob. 9ECh. 7.1 - Prob. 10E
Ch. 7.1 - Prob. 11ECh. 7.1 - Prob. 12ECh. 7.1 - Prob. 13ECh. 7.1 - Prob. 14ECh. 7.1 - Prob. 15ECh. 7.1 - Prob. 16ECh. 7.1 - Prob. 17ECh. 7.1 - Prob. 18ECh. 7.1 - Prob. 19ECh. 7.1 - Prob. 20ECh. 7.1 - Prob. 21ECh. 7.1 - Prob. 22ECh. 7.1 - Prob. 23ECh. 7.1 - Prob. 24ECh. 7.1 - Prob. 25ECh. 7.1 - Prob. 26ECh. 7.1 - Prob. 27ECh. 7.1 - Prob. 28ECh. 7.1 - Prob. 29ECh. 7.1 - Prob. 30ECh. 7.1 - Prob. 31ECh. 7.1 - Prob. 32ECh. 7.1 - Prob. 33ECh. 7.1 - Prob. 34ECh. 7.1 - Prob. 35ECh. 7.1 - Prob. 36ECh. 7.1 - Prob. 37ECh. 7.1 - Prob. 38ECh. 7.1 - Prob. 39ECh. 7.1 - Prob. 40ECh. 7.1 - Prob. 41ECh. 7.1 - Prob. 42ECh. 7.1 - Prob. 43ECh. 7.1 - Prob. 44ECh. 7.1 - Prob. 45ECh. 7.1 - Prob. 46ECh. 7.1 - Prob. 47ECh. 7.1 - Prob. 48ECh. 7.1 - Prob. 49ECh. 7.1 - Prob. 50ECh. 7.1 - Prob. 51ECh. 7.1 - Prob. 52ECh. 7.1 - Prob. 53ECh. 7.1 - Prob. 54ECh. 7.1 - Prob. 55ECh. 7.1 - Prob. 56ECh. 7.1 - Prob. 57ECh. 7.1 - Prob. 58ECh. 7.1 - Prob. 59ECh. 7.1 - Prob. 60ECh. 7.1 - Prob. 61ECh. 7.1 - Prob. 63ECh. 7.1 - Prob. 64ECh. 7.1 - 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