Ease Into Prep with an SAT^® Question of the Day

Since the graphs of the given system of equations intersect at one point, there is only one solution. Set the equations equal to each other and then use the discriminant, b² − 4ac, to find the value of z.
12 = −x² + 8x + z
0 = −x² + 8x + z − 12

Recall that there is one solution when b² − 4ac = 0. Plug in a = −1, b = 8, and c = z − 12 into the discriminant formula and solve for z.
(8)² − 4(−1)(z − 12) = 0
64 + 4z −12 = 0
4z − 12 = −64
z − 12= −16
z = −4
The given system of equations intersect when z = −4. Choice (B) is correct.