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• The axis of symmetry is x =______.
­b/(2a)
• The vertex has x­coordinate ______. Substitute x back in to find y.
<
• The parabola opens up when a__0 and opens down when a___0. >
minimum
maximum
• The vertex is a ______________ when the parabola opens up and a ______________ when the parabola opens down.
c
• The y­intercept is located at (0, _____).
<
>
• The parabola is narrower than the parent graph y=x2 if |a|___1 and wider if |a|____1.
a/1
• The slope ______ will find points on the parabola that are 1 unit to the right and left of the vertex.
3
Example 1 Graphing in the form y­intercept:
a= b= c=
Opens up or down?
Axis of symmetry: Vertex:
Reflect the y­int over the axis of symmetry to find another point.
Use "a" to find points 1 unit to the right and left of the vertex.
Is the vertex a max or min?
4
On your whiteboard...
Axis of symmetry: x=2
Vertex: (2,­2)
y­intercept: (0,2)
Coordinates of four more points:
(3,­1) (1,­1) (4,2) (5,7) (­1,7)
5
Example 2 Graphing in the form y­intercept:
a= b= c=
Opens up or down?
Axis of symmetry: Vertex:
Use "a" to find points 1 unit to the right and left of the vertex.
Since the vertex is also the y­intercept, you can't reflect it to find another guide point. Instead, use another value for x to find a point and then reflect it over the axis of symmetry.
Is the vertex a max or min?
6
On your whiteboard...
Axis of symmetry:
x=0
Vertex:(0,3)
y­intercept: (0,3)
Coordinates of four more points: (1,3.33) (­1,3.33) (3,6) (­3,6)
7
Example 3 Application problem
A woodland jumping mouse hops along a parabolic path given by , where x is the mouse's horizontal position (in feet) and y is the corresponding height (in feet). Can the mouse jump over a fence that is 3 feet high?
8