Quadratic, Linear and Exponential Functions

Front

What is a linear function?

Back

A linear function is a function that can be graphically represented as a straight line. It has the form y = mx + b, where m is the slope and b is the y-intercept.

Front

What is an exponential function?

Back

An exponential function is a mathematical function of the form y = a(b^x), where a is a constant, b is the base (a positive real number), and x is the exponent. It shows rapid growth or decay.

Front

What is a quadratic function?

Back

A quadratic function is a polynomial function of degree 2, typically in the form y = ax^2 + bx + c, where a, b, and c are constants and a ≠ 0.

Front

How can you identify a linear equation from its graph?

Back

A linear equation will produce a straight line when graphed. The slope is constant, and it has a y-intercept.

Front

What does the y-intercept represent in a function?

Back

The y-intercept is the point where the graph of the function crosses the y-axis, indicating the value of y when x = 0.

Front

What is the general form of a quadratic equation?

Back

The general form of a quadratic equation is y = ax^2 + bx + c, where a, b, and c are constants.

Front

What is the difference between linear and exponential growth?

Back

Linear growth increases by a constant amount, while exponential growth increases by a percentage of the current value, leading to faster growth over time.

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 (opening upwards or downwards).

Front

How do you find the equation of an exponential function from a table of values?

Back

To find the equation of an exponential function from a table, identify the base by examining the ratio of consecutive y-values and use the form y = a(b^x) to determine a.

Front

What is the standard form of a linear equation?

Back

The standard form of a linear equation is Ax + By = C, where A, B, and C are integers, and A should be non-negative.