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 'a' value in a quadratic function determine?

Back

The 'a' value determines the direction of the parabola: if 'a' is positive, the parabola opens upwards; if 'a' is negative, it opens downwards.

Front

What is the vertex of a quadratic function?

Back

The vertex is the highest or lowest point of the parabola, depending on whether it opens up or down.

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 a vertical translation in the context of quadratic functions?

Back

A vertical translation shifts the graph of the function up or down without changing its shape.

Front

What is a horizontal translation in the context of quadratic functions?

Back

A horizontal translation shifts the graph of the function left or right without changing its shape.

Front

What does a reflection over the x-axis do to a quadratic function?

Back

A reflection over the x-axis changes the sign of the 'a' value, flipping the parabola upside down.

Front

What is a compression in quadratic functions?

Back

A compression occurs when the graph of the function is squeezed vertically, making it narrower, typically by a factor of k where 0 < k < 1.

Front

What is a stretch in quadratic functions?

Back

A stretch occurs when the graph of the function is pulled vertically, making it wider, typically by a factor of k where k > 1.

Front

How do you identify the vertical shift in the function f(x) = -(x + 3)² - 5?

Back

The vertical shift is down 5, as indicated by the -5 in the equation.