Vertex Form Quadratics

Front

What is the vertex form of a quadratic equation?

Back

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

Front

How do you identify the vertex from the vertex form of a quadratic equation?

Back

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

Front

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

Back

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

Front

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

Back

A positive 'a' value indicates that the parabola opens upwards.

Front

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

Back

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

Front

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

Back

Changing the 'h' value translates the graph horizontally; if h increases, the graph shifts to the right, and if h decreases, it shifts to the left.

Front

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

Back

Changing the 'k' value translates the graph vertically; if k increases, the graph shifts up, and if k decreases, it shifts down.

Front

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

Back

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

Front

What does it mean to reflect a graph across the x-axis?

Back

Reflecting a graph across the x-axis means that for every point (x, y) on the graph, there is a corresponding point (x, -y).

Front

What does it mean to stretch a graph vertically?

Back

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