Flashcard on the standard AII.1 - AII.12 - 1O,4O - Dec 12 2024

Front

What is the standard form of a quadratic function?

Back

The standard form of a quadratic function is f(x) = ax² + bx + c, where a, b, and c are constants.

Front

What does it mean for a function to reflect over the x-axis?

Back

Reflecting over the x-axis means that for every point (x, y) on the graph of the function, the point (x, -y) will also be on the graph.

Front

What is a vertical stretch in a function?

Back

A vertical stretch occurs when the output values of a function are multiplied by a factor greater than 1, making the graph taller.

Front

How do you find the composition of two functions, g(f(x))?

Back

To find g(f(x)), you first evaluate f(x) and then substitute that result into g.

Front

What is the vertex form of a quadratic function?

Back

The vertex 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 it mean for a function to undergo a horizontal shift?

Back

A horizontal shift occurs when the graph of a function is moved left or right along the x-axis.

Front

What is the significance of the 'a' value in a quadratic function?

Back

The 'a' value determines the direction of the parabola (upward if a > 0, downward if a < 0) and its width (narrower if |a| > 1, wider if |a| < 1).

Front

What is the process to simplify the expression 25x²y³?

Back

To simplify, ensure all like terms are combined and expressed in the simplest form, which in this case is already simplified.

Front

What does it mean for a function to be vertically compressed?

Back

A vertical compression occurs when the output values of a function are multiplied by a factor between 0 and 1, making the graph shorter.

Front

How do you determine the transformations of a function from its equation?

Back

Analyze the equation for changes in the coefficients and constants to identify shifts, stretches, and reflections.