SAT Math Problem (19)

Question

The function g(x) = ax³+bx²+cx+d has zeroes x = -2, 3, 6. If g(0) < 0, which of the following must also be negative?

 

A. g(-3)

B. g(-1)

C. g(4)

D. g(5)

Answer 1

If g(0) < 0, then g(0) is on the "valley" containing a relative minimum between g(-2) and g(3).

g(-1) is the only value within that interval.

Answer 2

Sketch the graph beginning by placing POINTS on the numberline at x = -2, 3 and 6.

Also place a dot BELOW the numberline beneath x=0.

Now sketch the smooth polynomial graph, passing from -2 down through the point (0, -something), then back up to the x-axis at x=3, continuing up for a while, then down through x=6 and thence continuing further downward forever.

 

your sketch shows that g(-1) must be negative.