Name____________________________________
Date ___________
Period ________
Unit 8 Notes 2
Quadratic Equations
Equation
Table
Look for the symmetry in the
X
Y
I DO EX 1:
Graph
table.
On the set of axis below, draw the graph of y  x2  4 x  3 .
Determine the roots, vertex, orientation, minimum/maximum,
axis of symmetry.
Roots:
Vertex:
Axis of Symmetry:
Is the graph a minimum or
maximum?
What is the orientation?
Equation
Graph
Table
WE DO EX 2:
On the set of axis below, draw the graph of y = -x2 + 2x + 3.
Using the graph, determine the roots, orientation, vertex, and
minimum/maximum point of y = -x2 + 2x + 3.
Application Concept/Content
Roots:
Vertex:
Axis of Symmetry:
Is the graph a minimum or
maximum? Explain.
What is the orientation?
Contrast the equation and graph in EX 1 with the equation and graph in EX 2.
WE DO:
For each quadratic equation below: Enter the equation into y =
Look at the graph to see where the roots would be
found. (positive or negative)
Use the table to help you find the information stated.
EX3. y = x2 + 6 x + 8
X
-6
-5
-4
-3
-2
0
Y
8
3
0
-1
0
8
Using the table:
What are the roots?
What is the vertex point?
Write the equation for the axis of symmetry.
EX4. y = -x2 –2x – 4
Roots:
X
Y
Vertex:
Axis of Symmetry:
YOU DO EX 5:
On the set of axis below, draw the graph of y = x2 – 4x – 5. Using the graph, determine the
orientation, vertex, axis of symmetry and roots of y = x2 – 4x – 5.
Be sure to use multiple representations (equation, graph, & table) like in the previous examples!
________1. What are the vertex and axis of________2. The equation
symmetry of the parabola
is graphed on
the set of axes below.
?
1) vertex: (8, -1); axis of symmetry: x = 8
2) vertex: (8, 1); axis of symmetry: x = 8
3) vertex: (-8, -1); axis of symmetry: x = -8
4) vertex: (-8, 1); axis of symmetry: x = -8
Based on this graph, what are the roots of the
equation
?
1) 8 and 0
2) 2 and -4
3) 9 and -1
4) 4 and -2
3. Graph the equation y = x2 – 2x – 3 on the accompanying set of axes. Using the graph,
determine the roots, vertex, and axis of symmetry of the equation x2 – 2x – 3 = 0.
Equation
Graph
Table
HW 1:
On the set of axis below, draw the graph of y = -x2 – 6x + 7.
Using the graph, determine the roots, orientation, vertex, and
axis of symmetry of y = -x2 – 6x + 7.
Application Concept/Content
Roots:
Orientation:
Vertex:
Axis of Symmetry: