Quadratic transformations

Front

What is the vertex form of a quadratic function?

Back

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

Front

Identify the vertex of the function f(x) = -2(x + 1)² + 3.

Back

The vertex is (-1, 3).

Front

How does the equation f(x) = (x + 3)² + 4 transform the parent function f(x) = x²?

Back

It shifts the graph 3 units left and 4 units up.

Front

What does a negative 'a' value in the vertex form indicate about the parabola?

Back

A negative 'a' value indicates that the parabola opens downwards.

Front

What is the effect of changing 'k' in the vertex form f(x) = a(x - h)² + k?

Back

Changing 'k' shifts the graph vertically; increasing 'k' moves it up, while decreasing 'k' moves it down.

Front

What transformation does the equation y = (x - 4)² represent compared to y = x²?

Back

It represents a horizontal shift 4 units to the right.

Front

What does the term 'vertical stretch' mean in the context of quadratic functions?

Back

A vertical stretch occurs when the 'a' value in the vertex form is greater than 1, making the parabola narrower.

Front

If f(x) = 2(x - 1)² + 3, what transformations are applied to the parent function?

Back

The graph is vertically stretched by a factor of 2, shifted right 1 unit, and shifted up 3 units.

Front

What is the effect of a vertical compression on a quadratic function?

Back

A vertical compression occurs when the 'a' value is between 0 and 1, making the parabola wider.

Front

How do you determine the direction in which a parabola opens?

Back

The direction is determined by the sign of 'a' in the vertex form: if 'a' is positive, it opens upwards; if negative, it opens downwards.