Quadratic Transformations

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 and a ≠ 0.

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 parabola?

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 a vertical shift in the context of quadratic transformations?

Back

A vertical shift occurs when a constant is added to or subtracted from the function, moving the graph up or down without changing its shape.

Front

What is a horizontal shift in the context of quadratic transformations?

Back

A horizontal shift occurs when the input variable x is replaced with (x - h) or (x + h), moving the graph left or right.

Front

What is a vertical stretch or compression?

Back

A vertical stretch occurs when the coefficient 'a' is greater than 1, making the parabola narrower, while a compression occurs when 0 < a < 1, making it wider.

Front

What is a reflection in the context of quadratic functions?

Back

A reflection occurs when the coefficient 'a' is negative, flipping the parabola over the x-axis.

Front

How does the equation g(x) = -4x² transform the parent function f(x) = x²?

Back

It reflects the graph across the x-axis and stretches it vertically by a factor of 4.

Front

What transformation does g(x) = x² + 21 represent?

Back

It represents a vertical shift of the graph of f(x) = x² upwards by 21 units.