GRAPHING PARABOLASThis presentation is modified from a HyperStudio presentation.

Annette WilliamsMTSU

Another form of the equation for a parabola is :

khxaxf 2

In this form, (h , k) is the vertex of the parabola. For example, in the equation

(4, –5) is the vertex. Notice that to write h the sign in front of it in the formula changes, but on k it does not.

543 2 xxf

Write the vertex for each equation.

18

622

764

2

2

2

xxg

xxf

xy Vertex is: (–6, –7)

Vertex is:(–2, –6)

Vertex is:(8, 1)

Parabola in the form f(x) = a(x - h)2 + k If a is positive the parabola opens up. If a is negative the parabola opens down. The vertex is (h, k). The axis of symmetry is the line x = h. The minimum value is k when the parabola opens up. The maximum value is k when the parabola opens down.  The range is y > k when the parabola opens up.The range is y < k when the parabola opens down.

Find the axis of symmetry, minimum or maximum value, and range of each parabola.

18

622

764

2

2

2

xxg

xxf

xy

Axis is x = -6, minimum value is -7, range is y > -7.

Axis is x = -2, maximum value is -6, range is y < -6.

Axis is x = 8, maximum value is 1, range is y < 1.

7)6(4 2 xy

6)2(2)( 2 xxf

1)8()( 2 xxg