If the two points (1,d),(−1,e)(1, d), (-1, e)(1,d),(−1,e) are on the graph of y=ax2+bx+cy = a x^2 + b x + cy=ax2+bx+c, and e−d=−6e - d = -6e−d=−6, then bbb equals: −3-3−3 000 333 ac\sqrt{ac}ac a+c2\frac{a+c}{2}2a+c Solution Plug the two given points into the quadratic: (1,d):a+b+c=d,(−1,e):a−b+c=e, \begin{aligned} (1, d) &:& a + b + c &=& d, \\ (-1, e) &:& a - b + c &=& e, \end{aligned} (1,d)(−1,e)::a+b+ca−b+c==d,e, subtract: 2b=d−e=62b=6b=3 \begin{aligned} 2b &=& d - e = 6 \\ 2 b &=& 6 \\ b &=& 3 \end{aligned} 2b2bb===d−e=663 The answer is c.