Problem: If the points (1,y1)\left(1, y_{1}\right)(1,y1) and (−1,y2)\left(-1, y_{2}\right)(−1,y2) lie on the graph of y=ax2+bx+cy=a x^{2}+b x+cy=ax2+bx+c, and y1−y2=−6y_{1}-y_{2}=-6y1−y2=−6, then bbb equals:
Answer Choices:
A. −3-3−3
B. 000
C. 333
D. ac\sqrt{\mathrm{ac}}ac
E. a+c2\dfrac{a+c}{2}2a+c Solution:
y1=a+b+cy_{1}=a+b+cy1=a+b+c and y2=a−b+c∴y1−y2=2by_{2}=a-b+c \quad \therefore y_{1}-y_{2}=2 by2=a−b+c∴y1−y2=2b. Since y1−y2=−6,2b=−6,b=−3y_{1}-y_{2}=-6,2 b=-6, b=-3y1−y2=−6,2b=−6,b=−3.