Linear, Exponential, and Quadratic 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 f(x) = a * b^x, where a is a constant, b is the base (a positive real number), and x is the exponent.

Front

What is a quadratic function?

Back

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

Front

How do you identify the slope of a linear function from its equation?

Back

The slope of a linear function can be identified from its equation in the form y = mx + b, where m represents the slope.

Front

What does the y-intercept represent in a linear function?

Back

The y-intercept is the point where the graph of the function crosses the y-axis, represented by the value of b in the equation y = mx + b.

Front

What is the general form of a quadratic equation?

Back

The general form of a quadratic equation is ax^2 + bx + c = 0, where a, b, and c are constants.

Front

How can you determine if a function is linear or exponential based on a table of values?

Back

If the differences between consecutive y-values are constant, the function is linear. If the ratios of consecutive y-values are constant, the function is exponential.

Front

What is the significance of the slope in a linear function?

Back

The slope indicates the rate of change of the function; a positive slope means the function is increasing, while a negative slope means it is decreasing.

Front

How do you find the equation of a linear function given two points?

Back

To find the equation, calculate the slope (m) using the formula m = (y2 - y1) / (x2 - x1), then use one of the points to solve for b in y = mx + b.

Front

What is the vertex of a quadratic function?

Back

The vertex is the highest or lowest point of the parabola represented by the quadratic function, found using the formula x = -b/(2a) for the x-coordinate.