Transformation of Quadratic Functions

Front

What is a quadratic function?

Back

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

Front

What is the parent function of quadratic functions?

Back

The parent function of quadratic functions is f(x) = x².

Front

What does the term 'vertex' refer to in a quadratic function?

Back

The vertex is the highest or lowest point of the parabola represented by the quadratic function.

Front

What is the effect of a positive 'a' value in a quadratic function?

Back

A positive 'a' value opens the parabola upwards.

Front

What is the effect of a negative 'a' value in a quadratic function?

Back

A negative 'a' value opens the parabola downwards.

Front

What does a vertical shift in a quadratic function do?

Back

A vertical shift moves the graph up or down without changing its shape.

Front

What does a horizontal shift in a quadratic function do?

Back

A horizontal shift moves the graph left or right without changing its shape.

Front

What is the effect of adding a constant to the function, like in f(x) = x² + k?

Back

Adding a constant k shifts the graph vertically; if k is positive, it shifts up, and if negative, it shifts down.

Front

What does the expression (x - h)² represent in a quadratic function?

Back

The expression (x - h)² represents a horizontal shift to the right by h units.

Front

What does the expression (x + h)² represent in a quadratic function?

Back

The expression (x + h)² represents a horizontal shift to the left by h units.