If the graph goes up from left to right, the function is increasing. If it goes down, it's decreasing.

Concave up looks like a smile, concave down looks like a frown.

A steeper slope indicates a larger rate of change (either increasing or decreasing more rapidly).

Draw a secant line between the two points and find its slope.

It indicates that the rate of change is zero.

The steepness of the curve indicates the magnitude of the average rate of change; the direction indicates whether it's increasing or decreasing.

The graph is a parabola opening upwards. The rate of change is negative for $x < 0$, zero at $x = 0$, and positive for $x > 0$.

The graph is a parabola opening downwards. The rate of change is positive for $x < 0$, zero at $x = 0$, and negative for $x > 0$.

The vertex is the point where the graph changes direction (minimum or maximum point).

A graph that opens upwards is concave up, and a graph that opens downwards is concave down.

A function with a constant rate of change (slope), resulting in a straight line.

A function with a changing rate of change, creating a curved graph.

The change in output divided by the change in input over a specific interval.

A line that connects two points on a curve.

The direction of the curve of a function (either concave up or concave down).

The function is increasing at an increasing rate.

The function is increasing at a decreasing rate.

It is constant and equal to the slope of the line.

It changes as you move along the curve.

The rate of change of a quadratic function is linear.

$\frac{f(b) - f(a)}{b - a}$

$\frac{f(b) - f(a)}{b - a}$

$x = \frac{-b}{2a}$

$\frac{\Delta y}{\Delta x} = \frac{f(x_2) - f(x_1)}{x_2 - x_1}$

$a$

$a(x_1 + x_2) + b$

$m_{sec} = \frac{f(x+h)-f(x)}{h}$

Average rate of change is equivalent to the difference quotient: $\frac{f(x_2)-f(x_1)}{x_2-x_1}$

$\lim_{h \to 0} \frac{f(x+h)-f(x)}{h}$

$y = mx + b$