Parabolas in Vertex Form

A parabola is a U-shaped curve that is the graph of a quadratic function. It can open upwards or downwards.

The vertex is the highest or lowest point of the parabola, depending on its orientation.

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

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

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

The axis of symmetry divides the parabola into two mirror-image halves.

If 'a' is positive, the parabola opens up; if 'a' is negative, it opens down.

The maximum or minimum value occurs at the vertex: it's the y-coordinate of the vertex.

You can complete the square to convert a quadratic equation from standard form (ax² + bx + c) to vertex form.

The y-intercept is the point where the parabola crosses the y-axis, found by setting x = 0 in the equation.