Translations

Front

What is a quadratic function?

Back

A quadratic function is a polynomial function of degree 2, typically in the form y = ax² + bx + c, where a, b, and c are constants.

Front

What does the vertex form of a quadratic function look like?

Back

The vertex form of a quadratic function is y = a(x - h)² + k, where (h, k) is the vertex of the parabola.

Front

What transformation does the equation y = (x - 3)² - 2 represent?

Back

The equation represents a translation of the graph 3 units to the right and 2 units down.

Front

How does changing the value of 'a' in y = a(x - h)² + k affect 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 < 0, the parabola opens downwards.

Front

What is the standard form of a quadratic function?

Back

The standard form of a quadratic function is y = ax² + bx + c.

Front

What does the term 'translation' mean in the context of graph transformations?

Back

Translation refers to shifting a graph horizontally or vertically without changing its shape.

Front

What is the effect of adding a constant to the function y = x²?

Back

Adding a constant shifts the graph vertically. For example, y = x² + 3 shifts the graph up by 3 units.

Front

What does the equation y = (x + 4)² represent in terms of transformations?

Back

The equation represents a translation of the graph 4 units to the left.

Front

How do you identify the vertex of a quadratic function in vertex form?

Back

In vertex form y = a(x - h)² + k, the vertex is the point (h, k).

Front

What is the axis of symmetry for the quadratic function y = ax² + bx + c?

Back

The axis of symmetry is given by the formula x = -b/(2a).