SOLUTION: What's the equation of the parabola {{{ y = ax^2 + bx + c }}} which passes through the points of (0, 3), (1,4), and (2, 3)? A.) y = -(¼)x2 + (½)x + 3 B.) y = -(⅔)x2 + (5/

Algebra ->  Test  -> Lessons -> SOLUTION: What's the equation of the parabola {{{ y = ax^2 + bx + c }}} which passes through the points of (0, 3), (1,4), and (2, 3)? A.) y = -(¼)x2 + (½)x + 3 B.) y = -(⅔)x2 + (5/      Log On


   

Question 1077218: What's the equation of the parabola +y+=+ax%5E2+%2B+bx+%2B+c+ which passes through the points of (0, 3), (1,4), and (2, 3)?
A.) y = -(¼)x2 + (½)x + 3
B.) y = -(⅔)x2 + (5/3)x + 3
C.) y = 2x2 - 13x + 21
D.) y = -x2 + 2x + 3
Answer by MathLover1(20849) About Me  (Show Source):
You can put this solution on YOUR website!

What's the equation of the parabola y=ax%5E2%2Bbx%2Bc which passes through the points of (0, 3), (1,4), and (2,+3)?
use given points to find a,b,and c
y=ax%5E2%2Bbx%2Bc...............for point (0, 3)
3=a%2A0%5E2%2Bb%2A0%2Bc
3=c.........eq.1
y=ax%5E2%2Bbx%2Bc............for 3=c and (1,4)
4=a%2A1%5E2%2Bb%2A1%2B3
4=a%2Bb%2B3
1=a%2Bb.........solve for a
a=1-b..........eq.2
y=ax%5E2%2Bbx%2Bc............3=c,a=1-b, and (2, 3)
3=%281-b%292%5E2%2Bb%2A2%2B3
3-3=%281-b%294%2B2b
0=4-4b%2B2b
0=4-2b
2b=4
b=2........eq.3
find a
a=1-b..........eq.2
a=1-2
a=-1
so, your equation is:
y=-x%5E2%2B2x%2B3
and your answer is: D.) y=-x%5E2%2B2x%2B3