Vertex form and standard form

Given:

The vertex of a quadratic function is (-5,-1) and it passes through the point (-2,2).

To find:

The vertex and standard form of the quadratic function.

Solution:

The vertex form of a quadratic function is:

Where, a is a constant, (h,k) is vertex.

The vertex of a quadratic function is (-5,-1). It means .

            ...(i)

The quadratic function passes through the point (-2,2). Putting in (i), we get

Putting in (i), we get

Therefore, the vertex for of the quadratic function is .

The standard form of a quadratic function is:

We have,

Therefore, the standard form of a quadratic function is .