Vertex Form Quadratics

Front

What is the vertex form of a quadratic function?

Back

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

Front

What does the 'a' value in vertex form indicate?

Back

The 'a' value indicates the direction of the parabola (upward if a > 0, downward if a < 0) and the width of the parabola (narrower if |a| > 1, wider if |a| < 1).

Front

How does a positive 'a' value affect the graph of a quadratic function?

Back

A positive 'a' value causes the parabola to open upwards.

Front

How does a negative 'a' value affect the graph of a quadratic function?

Back

A negative 'a' value causes the parabola to open downwards.

Front

What transformation does the expression (x-h) represent in vertex form?

Back

The expression (x-h) represents a horizontal shift of the graph h units to the right if h is positive and to the left if h is negative.

Front

What transformation does the '+k' represent in vertex form?

Back

The '+k' represents a vertical shift of the graph k units up if k is positive and down if k is negative.

Front

What is the axis of symmetry in a quadratic function in vertex form?

Back

The axis of symmetry is the vertical line x = h, where (h, k) is the vertex.

Front

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

Back

The vertex can be found directly from the vertex form f(x) = a(x-h)² + k as the point (h, k).

Front

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

Back

A vertical stretch occurs when the absolute value of 'a' is greater than 1, making the parabola narrower.

Front

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

Back

A vertical shrink occurs when the absolute value of 'a' is less than 1, making the parabola wider.