Question

Find the equation of the parabola that passes through the points (0,1), (1,5), and (2,3). Show your work using Algebra or use a Quadratic Regression.

A) y = 2x^2 - 2x + 1
B) y = -x^2 + 3x + 1
C) y = x^2 - 2x + 1
D) y = -2x^2 + 4x + 1

Answer 1

To find the equation of the parabola passing through the points (0,1), (1,5), and (2,3), create a system of three equations using the general equation of a parabola. Solve the system of equations to find the equation of the parabola, which is y = 2x^2 - 2x + 1.

Step-by-step explanation:

To find the equation of the parabola passing through the points (0,1), (1,5), and (2,3), we can create a system of three equations using the general equation of a parabola, y = ax^2 + bx + c. Substituting each point into the equation, we get the following three equations:

1 = c

5 = a + b + c

3 = 4a + 2b + c

Solving this system of equations, we find that the equation of the parabola is y = 2x^2 - 2x + 1. Therefore, option A is correct.