Question

Find the equation of a parabola passing through the points

(0,0), (2,0), and (1,1).
a) y=x²−3x+2
b) y=−x²+3x
c) y=x²−x
d) y=−x²+x

Answer 1

To find the equation of a parabola passing through given points, we can solve a system of equations to obtain the values of a, b, and c. Substituting these values into the general form of the parabola equation gives the equation of the parabola.

Step-by-step explanation:

To find the equation of a parabola passing through the points (0,0), (2,0), and (1,1), we can use the general form of a parabola equation: y = ax^2 + bx + c. By substituting the coordinates of the given points into this equation, we can obtain a system of three equations:

Equation 1: 0 = c

Equation 2: 0 = 4a + 2b + c

Equation 3: 1 = a + b + c

By solving this system of equations, we can find the values of a, b, and c. Substituting the obtained values into the general form of the parabola equation, the equation of the parabola passing through the given points is y = x^2 - 3x + 2, option (a).