These 3 points are on a parabola defining the edge of a ski: (-4,1) (-2,0.94) (0,1)

Question

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

(-4,1)

(-2,0.94)

(0,1)

1. 

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

1. Repeat this process with the other 2 points to build a 2nd linear equation.
2. Record all three equations in the box below.

#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. Record your result here.

#4Use the inverse matrix to solve the system of equations. 

Answer 1

(-4,1) and (0,1) are symmetrical about the line x=-2, the average of the 2 x coordinates -4 and 0

3rd point is (-2,.94) which is on the line of symmetry, it helps to plot the points

y = ax^2 +bx + c

plug in the 3 points to get a system of 3 equations 3 unknowns, a,b, and c

1= 16a -4b + c

1= a(0^2) +0(b) + c

c=1

.94 = 4a -2b + c

.94-1 = 4a-2b

-.06 = 4a-2b

-.03 = 2a -b

4a -b = 0

4a -2b = -.06

b = .06

a = .06/4 = .015

y = .015x^2 +.06x + 1 is the parabola's equation

check the answer

1= .015(0^2)+.06(0)+1

1=1

1=.015(-4)^2 +.06(-4) +1

0 = .015(16) -.24

0= .24-.24

0=0

.94=.015(-2)^2 +.06(-2) +1

.94 = .015(4)- .12+1

.94= .06 -.12+1

.94= 1.06-.12

.94 = .94

a=.015

b= .06

c= 1

that's the solution using substitution elimination

but you should get the identical answer using matrix algebra