Vertex form of a quadratic function

Definition

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. It is useful for identifying the maximum or minimum point and the axis of symmetry.

5 Must Know Facts For Your Next Test

1. The vertex form makes it easy to find the vertex of the quadratic function.
2. In $y = a(x-h)^2 + k$, if $a > 0$, the parabola opens upwards; if $a < 0$, it opens downwards.
3. The value of $h$ represents the horizontal shift from the origin, while $k$ represents the vertical shift.
4. The axis of symmetry can be found at $x = h$.
5. Converting a quadratic function from standard form to vertex form involves completing the square.

Review Questions

Related terms

Standard Form:

A quadratic function written as $ax^2 + bx + c$, where $a$, $b$, and $c$ are constants.

Axis of Symmetry:

A vertical line that divides a parabola into two mirror images, represented by $x = h$ in vertex form.

Completing The Square: A method used to convert a quadratic equation into vertex form by adding and subtracting appropriate constants.