Local extrema: peaks and valleys in a specific region. Global extrema: absolute highest and lowest points of the entire graph.

Zeros: x-values where $f(x) = 0$. Critical points: x-values where $f'(x) = 0$ or $f'(x)$ is undefined.

Even: ends point in the same direction. Odd: ends point in opposite directions.

Root: where the graph intersects the x-axis. Turning point: local max or min.

Increasing: the function's value goes up as x increases. Decreasing: the function's value goes down as x increases.

Concavity: describes the curve's bend (up or down). Slope: describes the steepness and direction of the line tangent to the curve.

Zero: point where the graph crosses the x-axis. Inflection point: point where the concavity changes.

First derivative: gives the rate of change of the function. Second derivative: gives the rate of change of the first derivative (concavity).

Local maximum: the highest point in a specific region. Global maximum: the highest point on the entire graph.

Critical point: point where the derivative is zero or undefined. Endpoint: a point at the boundary of the function's domain.

Between two distinct real zeros of a polynomial, there must be at least one local maximum or minimum.

If positive, the function opens upwards (global minimum). If negative, the function opens downwards (global maximum).

Inflection points indicate where the rate of change of the function is changing its direction (increasing or decreasing).

A polynomial of degree 'n' can have at most n-1 turning points (local maxima or minima).

Critical points (where the derivative is zero or undefined) are potential locations of local maxima, local minima, or saddle points.

If the derivative is positive, the function is increasing. If the derivative is negative, the function is decreasing.

If the second derivative is positive, the function is concave up. If the second derivative is negative, the function is concave down.

End behavior describes what happens to the function's values as x approaches positive or negative infinity, determined by the leading term.

Zeros are where the function crosses the x-axis. Extrema are local max/min. Concavity describes the curve's bend. They all help define the shape of the polynomial.

Find critical points by taking the derivative and setting it to zero, then test intervals between these points to see if the derivative is positive (increasing) or negative (decreasing).

A function of the form $p(x) = a_nx^n + a_{n-1}x^{n-1} + ... + a_1x + a_0$, where 'n' is a non-negative integer and the 'a' values are real numbers.

The highest power of the variable in the polynomial.

A point on the graph of a function that is a peak within a specific region.

A point on the graph of a function that is a valley within a specific region.

The absolute highest point of the entire graph of a function.

The absolute lowest point of the entire graph of a function.

The x-values where the function crosses the x-axis (where $f(x) = 0$).

A point on a curve where the concavity changes (from concave up to concave down, or vice versa).

The coefficient of the term with the highest power in a polynomial.

The direction in which a curve bends. It can be concave up or concave down.