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Find real numbers a, b, and c so that the graph of the function y = ax² +bx+c contains the points (1,2), (-2,9), and (0,3).

Find real numbers a, b, and c so that the graph of the function y = ax² +bx+c contains the points (1,2), (-2,9), and (0,3).

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Find real numbers a, b, and c so that the graph of the function y = ax² + bx+c contains the points (1,2), (-2,9), and (0,3). Select the correct choice below and fill in any answer boxes within your choice. O A. The solution is a = b= and c = . (Type integers or simplified fractions.) B. There are infinitely many solutions. Using ordered triplets, they can be expressed as {(a,b,c) a= b= c any real number}. (Simplify your answers. Type expressions using c as the variable as needed.) O C. There are infinitely many solutions. Using ordered triplets, they can be expressed as {(a,b,c) a = b any real number, c any real number}. (Simplify your answer. Type an expression using b and c as the variables as needed.) O D. There is no solution.
Transcribed Image Text:Find real numbers a, b, and c so that the graph of the function y = ax² + bx+c contains the points (1,2), (-2,9), and (0,3). Select the correct choice below and fill in any answer boxes within your choice. O A. The solution is a = b= and c = . (Type integers or simplified fractions.) B. There are infinitely many solutions. Using ordered triplets, they can be expressed as {(a,b,c) a= b= c any real number}. (Simplify your answers. Type expressions using c as the variable as needed.) O C. There are infinitely many solutions. Using ordered triplets, they can be expressed as {(a,b,c) a = b any real number, c any real number}. (Simplify your answer. Type an expression using b and c as the variables as needed.) O D. There is no solution.
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