Can a parab ola have
both a minimum and
a m axim um point?
No. A para b o la e ith e r
opens upward and has a
minimum point or opens
downward and has a
maximum point.
What are good values
to choose for x when
making the table?
Choose values o f x th a t
make x 2 d ivis ib le by 3 so
th a t th e y -va lu e s w ill be
integers.
The h ighest or low est p o in t of a p arab o la is its vertex, w hich is on th e axis of symm etry.If a > 0 in y = ax2 + bx + c,
the parabola opens upward.
I
The vertex is the minimum point,
or lowest point, of the parabola.Pr o b l em 1
If a < 0 in y = a x 2 + b x + c,
the parabola opens downward.
I
The vertex is the maximum point,
or highest point, of the parabola.Identifying a Vert ex
What are the coordinates of the vertex of each graph? Is it a minimum or a maximum?Q H' .y uu
*y 4
lV j
r z \ £ \ J m
\^0 / X
* I ^ X J^1- o^2
The vertex is (0,3). It is a maximum.vj Got It? 1. What is the vertex of the graph
at the right? Is it a minimum or
a maximum?The vertex is (1, -1 ). It is a minimum., y&
X
§ 0(^7) J
You can use the fact that a parabola is symmetric to graph it quickly. First, find the
coordinates of the vertex and several points on one side of the vertex. Then reflect the
points across the axis of symmetry. For graphs of functions of the form y = ax2, the
vertex is at the origin. The axis of symmetry is the y-axis, or x = 0.
Pr o b l em 2 Gr ap h i n g y = a x 2
Graph the function y = | x 2. Make a table of values. What are the domain and range?
y = !*2
0 (0)2 = 0 ( 0 , 0 )
(^3) ^(3)2 = 3 ( 3 , 3 )
65 (6)2 = 12 ( 6 , 12 )
C[y 4f t
n W
■--
2 -( Ol 6 12
Reflect the points from the table
over the axis of symmetry, x = 0,
to find more points on the graph.
The domain is all real numbers. The range is y > 0.
Go t I t? 2. Graph the function y = -3 x 2. What are the domain and range?
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PowerAlgebra.com Lesso n 9- 1 Quadratic Graphs and Their Properties^547