Use MATLAB to find the coefficients of the quadratic polynomial y = ax2 + bx + c

Question

Use MATLAB to find the coefficients of the quadratic polynomial y = ax2 + bx + c that passes through the points (x, y) = (1, 4), (4, 73), (5, 120). Hint: consider this as a system of linear equations in terms of the variables a, b, and c.

The figure below shows traffic flows in vehicles per hour through six intersections of one?way streets. Traffic flow entering and leaving the area is shown. Can the unknown flows f1 f7 be found? If not, how many additional sensors are needed? Explain.

Any help would be greatly appreciated! Thanks so much!

Use MATLAB to find the coefficients of the quadratic polynomial y = ax2 + bx + c that passes through the points (x, y) = (1, 4), (4, 73), (5, 120). Hint: consider this as a system of linear equations in terms of the variables a, b, and c. The figure below shows traffic flows in vehicles per hour through six intersections of one?way streets. Traffic flow entering and leaving the area is shown. Can the unknown flows f1 f7 be found? If not, how many additional sensors are needed? Explain. Any help would be greatly appreciated! Thanks so much!

Explanation / Answer

clear all
clc
syms a b c eq(x,y)
eq(x,y)=-y+a*x^2+b*x+c;
eq1=eval(eq(1,4));
eq2=eval(eq(4,73));
eq3=eval(eq(5,120));
S=solve(eq1==0,eq2==0,eq3==0,a,b,c);
S.a
S.b
S.c

%Answer

ans =

6


ans =

-7


ans =

5

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