Lesson 9-1

Example 1 Graph Opens Upward
Use a table of values to graph y = x + 6x + 8.	
x	y	
-6	  8	
-5	  3	
-4	  0	
-3	-1	
-2	  0	
-1	  3	
  0	  8	

Graph these ordered pairs and connect
them with a smooth curve.

Example 2 Graph Opens Downward
a.  Use a table of values to graph y = -2x – 5x – 3	
x	y	
-4	-15	
-3	  -6	
-2	  -1	
-1	   0	
  0	  -3	
  1	-10	
  2	-21	

Graph these ordered pairs and connect
them with a smooth curve.

b.  What are the domain and range of this function?
		D:  {x x is a real number}
		R:  {y y  0}

Example 3 Vertex and Axis of Symmetry
Consider the graph of y = 5x – 4x + 1.
a.	Write the equation of the axis of symmetry.
In y = 5x – 4x + 1, a = 5 and b = -4. Substitute these values into the equation of the axis of symmetry.
x = -	Equation for the axis of symmetry of a parabola
x = - or 	a = 5 and b = -4
The equation of the axis of symmetry is x = .

b.	Find the coordinates of the vertex.
Since the equation of the axis of symmetry is x =  and the vertex lies on the axis, the x-coordinate for the vertex is .
y = 5x – 4x + 1	Original equation
y = 5 – 4 + 1	x = 
y =  –  + 1	Simplify.
y = 
The vertex is at (,).

c.	Identify the vertex as a maximum or minimum.
Since the coefficient of the xterm is positive, the parabola opens upward and the vertex is a minimum point.

d.	Graph the function.
You can use the symmetry of the parabola to help you draw its graph. On a coordinate plane, graph the vertex and the axis of symmetry. Choose a value of x other than . For example, choose 0 and find the y-coordinate that satisfies the equation.	
y = 5x – 4x + 1	Original equation
y = 5(0) – 4(0) + 1	Let x = 0
y = 1	Simplify.
Graph (0, 1). Since the graph is symmetrical about its axis of symmetry, you can find another point on the other side of the axis of symmetry. The point at (0, 1) is  unit to the left of the axis. Go  to the right of the axis and plot the point (, 1). Repeat this for several other points. Then sketch the parabola. 

Example 4 Match Equations and Graphs
Multiple-Choice Test Item
Which is the graph of y = -2x + 4x + 2?
A			B 	

C			D 	

Read the Test Item
You are given a quadratic equation, and you are asked to choose its graph.

Solve the Test Item
Since the equation y = -2x + 4x + 2 is in standard form, find the axis of symmetry.
x = -	Equation for the axis of symmetry of a parabola
x = - or 1	a = -2 and b = 4

The axis of symmetry is x = 1. Look at the graphs. Since only A and C have x = 1 as their axis of symmetry, you can eliminate choices B and D. Since the coefficient of the xterm is negative, the graph opens downward. Eliminate choice C. The answer is A.