Mathematics Exam Review

A set of flashcards for reviewing key mathematical concepts from recent lectures.

What do the expressions (3n - 6)(n - 2) simplify to?

3n² - 12n + 12

How does exponential growth compare to quadratic growth as x increases?

Exponential functions will eventually grow more rapidly than quadratic functions.

From the equation h(x) = -16x² + 12x + 4, what is the starting height, total velocity and the effect on gravity of the quadratic

-16x²- effect on gravity (ax²)

12x- total velocity (bx)

4- starting height

What is the maximum height reached by the gymnast? If the equation is h(x) = -4x² + 16x + 9

The maximum height reached is 9 feet.

What point on the revenue graph indicates maximum revenue?

The vertex of the graph indicates the maximum revenue.

What equation represents the area A of a rectangular exhibit as a function of width w, where the length is constrained as 200 feet? The lengths equation is (200-2w)

$$A(w) = w(200 -2w)

What do the expressions (3n - 6)(n - 2) simplify to?

(3n^2 - 12n + 12).

Given the exponential function y = 2^{x} and the quadratic function y = x^2, how do these functions compare as x increases?

The exponential function y = 2^{x} will eventually grow more rapidly than the quadratic function y = x^2.

From the equation h(x) = -16x^2 + 12x + 4, identify the effects of each term on the motion of the object represented by the equation.

The term -16x^2 represents the effect of gravity, 12x indicates total velocity, and 4 denotes the starting height.

In the function h(x) = -4x^2 + 16x + 9, determine the maximum height reached by the gymnast.

The maximum height reached is 9 feet.

For the revenue graph represented by the function R(x) = -2x^2 + 12x, what point indicates maximum revenue?

The vertex of the graph indicates the maximum revenue.