Transformations of Quadratic Functions 2023

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 term 'vertex' refer to in a quadratic function?

Back

The vertex is the highest or lowest point on the graph of a quadratic function, depending on the direction of the parabola.

Front

What is the standard form of a quadratic function?

Back

The standard form of a quadratic function is f(x) = ax² + bx + c.

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.

Front

What effect does changing the value of 'a' in f(x) = a(x - h)² + k have on the graph?

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 downward.

Front

What does the term 'axis of symmetry' mean in relation to quadratic functions?

Back

The axis of symmetry is a vertical line that divides the parabola into two mirror-image halves, given by the equation x = h in vertex form.

Front

How does a vertical shift affect the graph of a quadratic function?

Back

A vertical shift moves the graph up or down. For example, in f(x) = a(x - h)² + k, the value 'k' represents the vertical shift.

Front

What is a horizontal shift in a quadratic function?

Back

A horizontal shift moves the graph left or right. In f(x) = a(x - h)² + k, the value 'h' represents the horizontal shift.

Front

What does a negative 'a' value indicate about the graph of a quadratic function?

Back

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

Front

What is the effect of a vertical stretch on a quadratic function?

Back

A vertical stretch occurs when the absolute value of 'a' is greater than 1, making the parabola narrower.