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) = ax² + bx + c, where a, b, and c are constants.

Front

What does the graph of a quadratic function look like?

Back

The graph of a quadratic function is a parabola, which can open upwards or downwards depending on the sign of the coefficient 'a'.

Front

What is the vertex of a quadratic function?

Back

The vertex is the highest or lowest point of the parabola, depending on its orientation. It can be found using the formula (-b/2a, f(-b/2a)).

Front

What is the axis of symmetry in a quadratic function?

Back

The axis of symmetry is a vertical line that divides the parabola into two mirror-image halves, given by the equation x = -b/2a.

Front

What is the effect of changing the value of 'a' in f(x) = ax²?

Back

Changing 'a' affects the width and direction of the parabola. If |a| > 1, the parabola is narrower; if 0 < |a| < 1, it is wider. If 'a' is negative, the parabola opens downwards.

Front

What does a positive 'c' value indicate in a quadratic function?

Back

A positive 'c' value indicates that the graph of the function is shifted upwards by 'c' units.

Front

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

Back

A negative 'c' value indicates that the graph of the function is shifted downwards by 'c' units.

Front

How does the term (x - h)² affect the graph of a quadratic function?

Back

The term (x - h)² shifts the graph horizontally. If h is positive, the graph shifts to the right; if h is negative, it shifts to the left.

Front

What is the effect of a vertical shift in a quadratic function?

Back

A vertical shift moves the graph up or down. For example, f(x) = x² + k shifts the graph up by k units if k is positive and down if k is negative.

Front

What does the term 'stretch' mean in the context of quadratic functions?

Back

A stretch occurs when the value of 'a' is greater than 1, making the parabola narrower. A compression occurs when 0 < |a| < 1, making it wider.