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2
Max or min
point
on the parab
ola
x2 is the high
est
exponent te
rm
Ushape gra
ph
Vertical line
that cuts the
parabola in
half
y=ax2+bx+c
3
• The axis of symmetry is x =______.
• The vertex has xcoordinate ______. Substitute x back in to find y.
• The parabola opens up when a__0 and opens down when a___0.
• The vertex is a ______________ when the parabola opens up and a ______________ when the parabola opens down.
• The yintercept is located at (0, _____).
• The parabola is narrower than the parent graph y=x2 if |a|___1 and wider if |a|____1.
• The slope ______ will find points on the parabola that are 1 unit to the right and left of the vertex.
b/(2a)
b/(2a)
> <
minimum maximum
c
> <
a/1
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Example 1 Graphing in the form
a= b= c=Opens up or down?
Axis of symmetry:
Vertex:
Is the vertex a max or min?
yintercept:
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.
5
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)
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Example 2 Graphing in the form
a= b= c=
yintercept:
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.
Opens up or down?
Axis of symmetry:
Vertex:
Is the vertex a max or min?
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On your whiteboard...
Axis of symmetry:
Vertex:
yintercept:
Coordinates of four more points:
(0,3)
x=0
(0,3)
(1,3.33) (1,3.33) (3,6) (3,6)
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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?
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