Digital SAT · Math · Advanced Math. The idea in plain words, the rules to remember, the mistake to avoid and a worked example, written and checked by Mega Lecture.
A quadratic function has a parabola as its graph. It opens upward when a > 0 and downward when a < 0. The vertex is its lowest or highest point, so it gives the minimum or maximum value. The zeros (x-intercepts) are where the function equals 0, and the vertex lies halfway between them.
An exponential function, f(t) = a(b)t, multiplies by the same factor b in each unit of time. Here a is the starting value. If b > 1 the quantity grows; if 0 < b < 1 it decays.
Function notation questions ask you to substitute. For f(g(x)), evaluate the inner function first, then put that result into the outer one.
Giving the x-coordinate of the vertex when the question asks for the maximum or minimum value. The x-coordinate says where it happens; substitute it back to get the value itself.
Answer: The minimum value is −13 (at x = 3).
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