2230.32 – A Quadratic Question

If the two points (1,d),(−1,e)(1, d), (-1, e) are on the graph of y=ax2+bx+cy = a x^2 + b x + c, and e−d=−6e - d = -6, then bb equals:

  1. −3-3

  2. 00

  3. 33

  4. ac\sqrt{ac}

  5. a+c2\dfrac{a+c}{2}

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}

subtract:

2b=d−e=62b=6b=3\begin{aligned}2b &= d - e = 6 \\2 b &= 6 \\b &= 3\end{aligned}

The answer is c.