2.3 Linear, Quadratic or Exponential

Front

What is a quadratic function?

Back

A quadratic function is a polynomial function of degree 2, typically in the form f(x) = ax² + bx + c, where a, b, and c are constants and a ≠ 0.

Front

Identify the general form of a linear function.

Back

The general form of a linear function is f(x) = mx + b, where m is the slope and b is the y-intercept.

Front

What characterizes an exponential function?

Back

An exponential function is characterized by a constant base raised to a variable exponent, typically in the form f(x) = a * b^x, where a is a constant and b > 0.

Front

How can you identify a quadratic function from a table of values?

Back

A quadratic function will show a constant second difference in the y-values when the x-values are evenly spaced.

Front

What is the difference between linear and quadratic functions in terms of their graphs?

Back

Linear functions graph as straight lines, while quadratic functions graph as parabolas (U-shaped curves).

Front

What does it mean for a function to exhibit exponential growth?

Back

Exponential growth occurs when a quantity increases by a consistent percentage over equal intervals of time, resulting in a rapid increase.

Front

What is the vertex of a quadratic function?

Back

The vertex of a quadratic function is the highest or lowest point on the graph, depending on the direction of the parabola.

Front

How do you determine if a function is linear from a set of points?

Back

A function is linear if the change in y divided by the change in x (slope) is constant between any two points.

Front

What is the standard form of a quadratic function?

Back

The standard form of a quadratic function is f(x) = a(x - h)² + k, where (h, k) is the vertex of the parabola.

Front

What does the term 'exponential decay' refer to?

Back

Exponential decay refers to a decrease in quantity at a rate proportional to its current value, often modeled by f(x) = a * e^(-bx).