Vertex (algebraic)

My Definition

Key Characteristics

The following are true of a vertex (algebraic):

  • The vertex can be a minimum or maximum point.

  • For parabolas opening up or down, the x-value of the vertex is equidistant from the x values of the x-intercepts.

  • For parabolas opening up or down, the y-value of the vertex is equidistant from the y value of the focus and the closest point on the directrix.

  • For parabolas opening up or down, the x-value of the vertex is same as the x-value of all the points on the axis of symmetry.

  • The x-value can be found using the formula h = 
    -b2a
    for a parabola with the equation y = ax2 + bx + c.

  • The y-value can be found by using the x-value into the equation, y = ax2 + bx + c, and simplifying.

  • Similar statements can be made for parabolas opening to the left and right.




Example

Vertex (algebraic) example

Non-example

Vertex (algebraic) non-example

TEKS: A(6)(B), A(7)(A)