Question

POINTS!!!!!! HELP!!!!!!!

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

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

Answer 1

The standard form of the parabola is

y = 2 x² + 4 x + 3

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