GRAPHING PARABOLAS This presentation is modified from a HyperStudio presentation. Annette Williams...
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Transcript of GRAPHING PARABOLAS This presentation is modified from a HyperStudio presentation. Annette Williams...
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