SOLUTION: what is the parabola that passes through each set of points (0,5),(2,-3),(-1,12)

Question 807684: what is the parabola that passes through each set of points (0,5),(2,-3),(-1,12)

Answer by DrBeeee(684) (Show Source): You can put this solution on YOUR website!
Given:
(1) y = a*x^2 + bx + c
Find (a,b,c) given
three points on the parabola
(a) (0,5)
(b) (2,-3) and
(c) (-1,12)
First substitute point (a) into (1) and get
(2) 5 = a*0 + b*0 + c or
(3) 5 = 0 + 0 + c or
(4) c = 5
Now put (b) and c into (1) and get
(5) -3 = 4a + 2b + 5 or
(6) 4a + 2b = -8
Now put (c) and c into (1) and get
(7) 12 = a - b + 5 or
(8) a - b = 7
Now solve (6) and (8) simultaneously to get a and b as follows;
First add twice (8) to (6) to get
(9) 6a + 0 = 6 or
(10) a = 1
Now put a into (8) to get
(11) 1 - b = 7 or
(12) b = -6
Let's check these value using point (c)
Is (12 = 1*(-1)^2 -6*(-1) + 5)?
Is (12 = 1 +6 +5)?
Is (12 = 12)? Yes
Answer: The parabola is y = x^2 -6x +5.

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