Question

The following 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
Required:
a. Use the x- and y-values of 1 of the points to build a linear equation with 3 variables: A, B, and C.
b. Repeat this process with 1 of the other to build a 2nd linear equation.
c. Record your equation here. Repeat this process with the other point to build a 3rd equation.

Answer 1

9514 1404 393

Answer:

a) 16A -4B +C = 1

b) 4A -2B +C = 0.94

c) C = 1

Explanation:

Substitute the x- and y-values into the general form equation.

a. A(-4)² +B(-4) +C = 1

16A -4B +C = 1

__

b. A(-2)² +B(-2) +C = 0.94

4A -2B +C = 0.94

__

c. A(0)² +B(0) +C = 1

C = 1

_____

Additional comment

Solving these equations gives A=0.015, B=0.06, C=1. The quadratic is ...

0.015x² +0.06x +1 = y