Transformations of Quadratic Functions

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.

Front

What does the coefficient 'a' in a quadratic function affect?

Back

The coefficient 'a' affects the direction and width of the parabola. If 'a' is positive, the parabola opens upwards; if negative, it opens downwards. The larger the absolute value of 'a', the narrower the parabola.

Front

What is the vertex of a quadratic function?

Back

The vertex is the highest or lowest point of the parabola, depending on the direction it opens. It can be found using the formula x = -b/(2a) for the x-coordinate.

Front

What does the term 'vertical shift' mean in transformations?

Back

A vertical shift moves the graph of the function up or down. This is represented by adding or subtracting a constant from the function, e.g., f(x) + k.

Front

What does the term 'horizontal shift' mean in transformations?

Back

A horizontal shift moves the graph of the function left or right. This is represented by adding or subtracting a constant inside the function, e.g., f(x + h).

Front

What is a vertical stretch?

Back

A vertical stretch occurs when the coefficient 'a' in the quadratic function f(x) = a(x - h)^2 + k is greater than 1, making the parabola narrower.

Front

What is a vertical compression?

Back

A vertical compression occurs when the coefficient 'a' in the quadratic function f(x) = a(x - h)^2 + k is between 0 and 1, making the parabola wider.

Front

What does a negative 'a' value indicate in a quadratic function?

Back

A negative 'a' value indicates that the parabola opens downwards.

Front

How do you identify a horizontal compression?

Back

A horizontal compression occurs when the absolute value of the coefficient of x in the function f(x) = a(x - h)^2 + k is greater than 1.

Front

What is the effect of adding a constant to the x-value in a quadratic function?

Back

Adding a constant to the x-value results in a horizontal shift of the graph. For example, f(x + 3) shifts the graph 3 units to the left.