Graphing Quadratic Functions - Vertex Form

Front

What is the vertex form of a quadratic function?

Back

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

Front

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

Back

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

Front

What does the 'a' value in the 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 do you determine the axis of symmetry for a parabola in vertex form?

Back

The axis of symmetry for a parabola in vertex form y = a(x - h)² + k is the vertical line x = h.

Front

What is the range of a quadratic function in vertex form when a < 0?

Back

The range is (-∞, k] where (h, k) is the vertex.

Front

What is the range of a quadratic function in vertex form when a > 0?

Back

The range is [k, ∞) where (h, k) is the vertex.

Front

How do you convert a quadratic function from standard form to vertex form?

Back

To convert from standard form y = ax² + bx + c to vertex form, complete the square.

Front

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

Back

This represents a shift of the graph 2 units to the right and 3 units up.

Front

What is the effect of adding a constant outside the squared term in vertex form?

Back

Adding a constant outside the squared term shifts the graph vertically.

Front

What is the effect of subtracting a constant inside the squared term in vertex form?

Back

Subtracting a constant inside the squared term shifts the graph horizontally to the right.