The equation for a parabola has the form y = ax^2 + bx + c, where a, b, and c are constants and a≠0. Find an equation for the parabola that passes through the points (−1,−9), (−3,1), and (3,19).
y = ________________
just plug and chug:
a-b+c = -9
9a-3b+c = 1
9a+3b+c = 19
subtract the two bottom equations to get
6b = 18, so b=3
Now you have
a+c = -6
9a+c = 10
subtract these two, you have
8a=16, so a=2
and that makes c = -8
y = 2x^2 + 3x - 8