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 about the parabola?

Back

The 'a' value indicates the direction the parabola opens: if 'a' is positive, it opens upwards; if 'a' is negative, it opens downwards.

Front

How do you find the axis of symmetry from the vertex form?

Back

The axis of symmetry can be found using the formula x = h, where (h, k) is the vertex.

Front

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

Back

The term (x-h) represents a horizontal shift of the graph to the right by 'h' units.

Front

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

Back

The term +k represents a vertical shift of the graph upwards by 'k' units.

Front

If f(x) = 2(x-3)² + 1, what is the vertex of the parabola?

Back

The vertex is (3, 1).

Front

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

Back

A negative 'a' value reflects the parabola across the x-axis.

Front

How does changing 'a' from 1 to 3 affect the graph of the parabola?

Back

Changing 'a' from 1 to 3 makes the parabola narrower (it stretches vertically).

Front

What is the standard form of a quadratic function?

Back

The standard form of a quadratic function is f(x) = ax² + bx + c.

Front

How can you convert from vertex form to standard form?

Back

To convert, expand f(x) = a(x-h)² + k to the form ax² + bx + c.