Quadratic Transformations

Front

What is the vertex form of a quadratic function?

Back

f(x) = a(x-h)² + k, where (h, k) is the vertex.

Front

What transformation occurs when the graph of y = x² is changed to y = (x - 4)²?

Back

Shifted right 4 units.

Front

If f(x) = x², what is g(x) if g(x) = x² - 5?

Back

g(x) is a vertical translation down 5 units.

Front

What does the 'a' in the vertex form f(x) = a(x-h)² + k represent?

Back

The 'a' value determines the direction and width of the parabola.

Front

How do you find the vertex of the function y = (x + 4)² - 6?

Back

The vertex is (-4, -6).

Front

What transformation maps f(x) = x² to g(x) = (x + 4)²?

Back

A translation shifting f(x) 4 units to the left.

Front

What is the effect of a negative 'a' value in the vertex form of a quadratic function?

Back

It reflects the graph across the x-axis.

Front

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

Back

A translation moves the graph horizontally or vertically without changing its shape.

Front

What is the standard form of a quadratic function?

Back

f(x) = ax² + bx + c.

Front

How does changing the 'h' value in the vertex form affect the graph?

Back

Changing 'h' shifts the graph left or right.