Solving systems of equations

Question

These 3 points are on a parabola defining the edge of a ski:

(-4,1)

(-2,0.94)

(0,1)

The general form for the equation of a parabola is Ax^2+Bx+C=y

1.

Use the x- and y-values of 1 to build a linear equation with 3 variables: A, B, and C.

Repeat this process with the other 2 points to build a 2nd linear equation.

2.

Build a matrix equation that represents this system of equations

3.

Use a graphing calculator or other graphing utility to find the inverse of the coefficient matrix

4.

Use the inverse matrix to solve the system of equations. Record the equation of the parabola

Answer 1

1 = 16A -4B + C for (-4,1)

0.94 = 4A +2B + C for (2,0.94)

1 = 0+0+C for (0,1)

C=1

1=16A-4B

.94 =4A+2B

1.88 =8A+4B

2.88=24A

A =2.88/24 =0.12

A=0.12

1=16(0.12)-4B

4B = 1-1.92

B =-0.92/4 = -0.23

y = 0.12x^2 -0.23x + 1 is the parabola through the three points

| 16, -4 1| 1|

| 4, 2 1|.94|

| 0, 0, 1| 1|

=

| 0, -12, -3| -2.76|

| 1, .5,.25| .235 |

| 0, 0, 1 | 1 \

=

| 0, 1, .125| -.23 |

| 1, 0, -6 | .35 |

| 0, 0, 0 | 1 |

=

=

|1 0, 0 | .12 |

|0, 1, 0| -.23|

|0. 0. 1| 1 |

with luck no arithmetic mistakes