Question

A problem contains the points (0,0),(1,-2) and (-1,-4). What is the equation of this parabola in standard form?

Answer 1

Answer:

The general equation of the parabola     y = -3 x² + x

Step-by-step explanation:

Step(i):-

Given points are (0,0) , (1, -2) and ( -1 , -4 )

Given the standard parabola

                                y = ax²+ b x + c ...(i)

Passing through the point (0,0)

                              c = 0

Passing through the point (1,-2)

                            -2 = a(1) +b(1)

                   a + b = -2 ...(ii)

Passing through the point (-1, -4)

                        - 4 = a - b

               a - b = -4 ...(iii)

Step(ii):-

Adding (ii) and (iii) equations , we get

            2 a = -6

              a = - 3

substitute   a = - 3 in equation (ii)

       -3 + b =-2

             b = -2 + 3 = 1

Final answer:-

The general equation of the parabola

              y = ax²+ b x + c

             y = -3 x² + x + 0

             y = -3 x² + x