Graph Opens? (Minimum or
Maximum?)
minimum value of the function if a > 0
ex) a= 1
Up or Down? Why?
opens up if a > 0
ex) a= 1
or
maximum value of the function if a < 0
ex) a= -1
opens down if a < 0
ex) a= -1
Compare to the Parent Function
when a > 1, the parabola is steeper than the
parent function
ex) a= 2
Wider or Narrower?
narrower than the graph of y= x^2 if |a| > 1
ex) |a|= 4
when a < 1, the parabola is wider than the
parent function
ex) a= 1/2
wider if |a| < 1
ex) |a|= 1/5
Axis of Symmetry?
: the line that passes through the vertex and
divides the parabola into two symmetric parts
x= -b/2a
ex) y= 3x2+12x-8
axis of symmetry= -12/6= -2
Vertex?
: the lowest or highest point on a parabola
(x,y)
x= axis of symmetry
y= input x into the equation to figure out
ex) y= 3x2+12x-8
x= -2
y= 3(-2)2+12(-2)-8
= -20
(-2, -20)
Y-Intercept?
y-intercept of c
ex) y= 2x2-3x-5
y-int: -5
(0, -5)
Name a Sister Point
: the point which is at an equal distance from
the axis of symmetry with the y-intercept
The Y-Axis or other? (-b / 2a)
is the axis of symmetry the y-axis or not?
ex) y= x2
axis of symmetry= y-axis
ex) y= 4x2+16x-2
axis of symmetry= -16/8= -2
Name the ordered pair.
find out ordered pairs by plugging in values
for x into the equation.
ex) y= 2x2+7x+21
x= 2
y= 2(2)2+7(2)+21
= 43
(2, 43)
What is it? how do you know?
the y-intercept of a parabola is c from the
equation ax2+bx+c
Use the features of a parabola to
name an opposite point.
: the point which is at an opposite position
from x-axis with the y-intercept
ex) y-int: (1, 2)
opposite point: (1, -2)
Create an Example showing ALL
features
y= -3x2-2x-5
a) graph opens?
opens downward; has a maximum coordinate
point
b) compare to the parent function
narrower
c) axis of symmetry
-b/2a = 2/-6 = -2/6
d) vertex
(-2/6, y) input -3 as x into the equation y=
-3x2-2x-5 ; (-2/6, -14/3)
e) y-intercept
-5; (0,-5)
f) sister point?
(-2/3, -5); sister point of (0, -5) equal distance
from the axis of symmetry and vertex.
g) solve
x
-2
2
y
-13
-21
Name the X-intercepts. (only strategy
to date is factoring)
y= 2x2-3x-5
0= 2x2+3x-5
0= x2+3/2x- 5/2
5/2= x2+3/2x
(3/4)2+5/2 = x2+3/2x+(3/4)2
Graph using your GDC and
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