Quadratic Transformation Graphs

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 does the term 'transformation' mean in the context of graphs?

Back

Transformation refers to the changes made to the graph of a function, such as shifting, stretching, compressing, or reflecting.

Front

What is a vertical shift in a quadratic function?

Back

A vertical shift occurs when a constant is added or subtracted from the function, moving the graph up or down.

Front

What is a horizontal shift in a quadratic function?

Back

A horizontal shift occurs when a constant is added or subtracted from the variable x, moving the graph left or right.

Front

How does the equation y = (x - h)² + k transform the graph of y = x²?

Back

This equation shifts the graph of y = x² horizontally by h units and vertically by k units.

Front

What effect does changing the coefficient 'a' in y = ax² 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 downwards.

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 significance of the y-intercept in a quadratic function?

Back

The y-intercept is the point where the graph crosses the y-axis, found by evaluating the function at x = 0.