Page 600 - Algebra 1

L E S S O N Identifying Characteristics of
89
Quadratic Functions
Warm Up
1. Vocabulary The U-shaped graph of a quadratic function is
(84)
a(n) (ellipse, parabola).
For each quadratic function, tell whether the graph opens upward or downward.
2.y=-3x2 +x-11 3.y=-8-7x+x2 (84) (84)
4. Evaluate y = x2 - 4x + 5 for x = -3. (9)
5.MultipleChoice Whichofthesefunctionsisrepresentedby
y
6
4
2
x
-4
2
2
4
New Concepts
The vertex of a parabola is the highest or lowest point on a parabola. It is the parabola’s “turning point.”
The minimum of a function is the least possible value of a function and
the maximum of a function is the greatest possible value of a function. It
is the y-value of the lowest or highest point on the graph of a function. On a parabola, the minimum or maximum is the y-coordinate of the vertex.
Identifying the Vertex and the Maximum or Minimum
Give the coordinates of each parabola’s vertex. Then give the minimum or maximum value and the domain and range of the function.
(84)
A y = 2x B y = -2x
this graph?
C y=2x2 D y=-2x2
Math Reasoning
Justify Why is the vertex a minimum when the parabola opens upward and a maximum when the parabola opens downward?
Example
1
y
8
8
y = -x2+ 4x + 1
4
4
O
y
= x2- 4
x
O
x
-8
-4
-8
4
8
-8
-4
y
8
Online Connection www.SaxonMathResources.com
a.
SOLUTION
The vertex appears to be at
(0, -4). It is the lowest point, so the minimum of the function is -4. The domain is the set of all real numbers; the range is the set of all real numbers greater than or equal to -4.
b.
SOLUTION
The vertex appears to be at
(2, 5). It is the highest point, so the maximum of the function is 5. The domain is the set of all real numbers; the range is the set of all real numbers less than or equal to 5.
Lesson 89 585