Quadratic Functions - Vertex Form

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

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

Back

To convert from standard form f(x) = ax² + bx + c to vertex form, complete the square.

Front

What is the axis of symmetry in a quadratic function?

Back

The axis of symmetry is a vertical line that divides the parabola into two mirror-image halves, given by the formula x = -b/(2a).

Front

What are the roots of a quadratic function?

Back

The roots (or x-intercepts) are the values of x where the function f(x) = 0.

Front

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

Back

The 'a' value determines the direction of the parabola (upward if a > 0, downward if a < 0) and its width.

Front

What is the significance of the vertex in a quadratic function?

Back

The vertex represents the maximum or minimum point of the parabola, depending on the direction it opens.

Front

How can you find the vertex from the standard form of a quadratic function?

Back

The vertex can be found using the formula (h, k) where h = -b/(2a) and k = f(h).

Front

What is the formula for finding the vertex from the vertex form?

Back

In vertex form f(x) = a(x - h)² + k, the vertex is directly given as (h, k).

Front

What is the relationship between the roots and the vertex of a parabola?

Back

The vertex lies on the axis of symmetry, which is equidistant from the roots of the parabola.

Front

What is the effect of changing the 'k' value in the vertex form?

Back

Changing the 'k' value shifts the parabola vertically up or down.