Do the following for the points 41022231 If you are entering

Do the following for the points (4,1),(0,2),(2,2),(3,1) (If you are entering decimal approximations, enter at least five decimal places.)

(a) Find the equation for the best-fitting parabola

(b) Find the equation for the best-fitting parabola with no constant term y=ax2+bx

a). equation of parabola y= ax^2 +bx +c

points are (4,1),(0,2),(2,2),(3,1)

(0,2)

2 = 0 +0+c

so c=2

y = ax^2 + bx+2

(2,2)

2 = 4a +2b +2

4a+2b=0

2a =-b

(3,-1)

-1 = 9a +3b +2

-3 = 9a + 3(-2a)

-3 =9a-6a

3a=-3

a=-1

2 =b

y = -x^2 +2x+2

b).

y=ax2+bx

(4,1),(0,2),(2,2),(3,1) points

(-4,-1)

-1 = 16a -4b

2= 4a +2b

2a+b =1

b = 1-2a

16a -4(1-2a) =-1

16a-4+8a=-1

24a = 3

a=1/8

b =1-2a = 1-2/8

=3/4