^{2}write this using each point as

^{2}

The parabola y=a+bx+cx^2 goes through the points (x, y)=(1, 4) and (2, 8) and (3, 14). Find and solve a matrix equation for the unknowns (a, b, c).

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Michael F. | Mathematics TutorMathematics Tutor

y=a+bx+cx^{2} write this using each point as

4= a+b+c for (1,4)

8= a+2b+4c for (2,8)

14=a+3b+9c for (3,14)

The matrix equation is a 3×3 matrix, a column of unknowns = a column vector of y's

1 1 1 | a 4

1 2 4 | b = 8

1 3 9 | c 14

The inverse matrix is

3 -3 1

-2.5 4 -1.5

.5 -1 .5

The unknown coefficients are

3 -3 1 | 4 2

-2.5 4 -1.5 | 8 = 1

.5 -1 .5 | 14 1

The curve is y = 2 + x + x^{2}

I have clearly not described the computation of the inverse matrix. I was lazy and did it using MINVERSE in EXCEL

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