Write the equation, in standard form, of the parabola containing the following points: (0, 1), (1, 5), (2, 3). You need to set up a system of three equations to get credit for this question.
A. y= -3x^2+7x+1
B.y= -7x^2+3x+1
C.y= -x^2+5x+3
D. y= 3x^2-7x-1 I think B but idk 4 of course first try (0,1) in each
Immediately it must be A or B to get 1 when x = 0
now try (1,5 ) in A and B
-3+7 + 1 = 5 okay
-7 + 3 + 1 = -3 Not possible
Better try (2,3) inA
-3*4 + 14 +1
-12+ 14 +1 = 3!!!! Caramba!!!! Now as they want
y = ax^2 + bx + c
(0,1) 1 = 0 + 0 + c so c = 1
then
y = ax^1 + bx + 1
(1.5) 5 = a + b + 1
so b = 4-a
then
y = ax^2 + (4-a)x + 1
(2,3) 3 =a *4 + (4-a) * 2 + 1
3 = 4a + 8 – 2a + 1
-6 = 2a
one = -3
b=4-a=7
c=1 What else new 🙂