POINTS Use quadratic regression to find the
equation for the parabola going
through these 3 points.
(2, 19) (6, 99) (-1, 1)

y=[?]^2+[?]x+[?]

The standard form of the parabola is

                   y = 2 x² + 4 x + 3

Step-by-step explanation:

Step(i):-

The standard form of the parabola

                                     y = a x² + b x + c ...(i)

The  equation for the parabola is passing through the point (2 , 19 )

                                 19 = 4a + 2b +c ...(ii)

The  equation for the parabola is passing through the point (6 , 99 )

                                 99 = 36a + 6b +c ...(iii)

The  equation for the parabola is passing through the point (-1,1) )

                                1 = a - b + c ...(iv)

step(ii):-

subtracting (ii) and (iii) , we get

                         8a + b = 20 ...(a)

Subtracting (iii) and (iv) , we get

                        5a + b = 14 ...(b)

solving (a) and (b) , we get

subtracting (a) and (b) , we get

                     8a + b-( 5a + b ) = 20 - 14

                     3 a = 6

                       a = 2

  substitute a=2 in equation (a) , we get

              8a + b = 20

              8(2) + b = 20

                     b =20 -16

                   b = 4

Substitute a= 2 ,b = 4 in equation (ii) , we get

                  19 = 4a + 2b +c

                  19 = 8 + 8  + C

              c = 19 -16 = 3

Final answer:-

The standard form of the parabola is

                   y = 2 x² + 4 x + 3