IM2 Transforming Quadratic Functions

A parabola is a U-shaped curve that can open upwards or downwards, defined by a quadratic function.

The vertex is the highest or lowest point of the parabola, depending on its direction.

Reflecting a parabola over the x-axis means flipping it upside down.

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

A negative coefficient causes the parabola to open downward.

A larger absolute value of the coefficient makes the parabola narrower, while a smaller absolute value makes it wider.

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

Translating a parabola 2 units down means moving every point on the graph down by 2 units.

A vertical stretch makes the parabola narrower.

The standard form is y = ax² + bx + c, where a, b, and c are constants.