Sewanhaka High School
Mrs. Lidowsky, Principal
Math 8
Mr. Long, Teacher
Per:______________
Date:________________________
Name:___________________________________
H.W. #35: Ditto
DO-NOW #35: Answer the following questions:
2) An image of a building in a photograph is 6
cm wide and 11 cm tall. If the image is similar
to the actual building and the actual building is
174 cm wide, how tall is the actual building, in
cm?
Topic: Graphing Quadratic Functions (Equations)
Main Idea: Graphing quadratic functions (equations)
Aim:
RECALL
Graph y = x – 5 using a table of values:
x y=x-5
y (x, y)
-4 ( ) – 5 =
( , )
-3 ( ) – 5 =
( , )
-2
-1
0
1
2
NOTES
Now graph the quadratic equation, y = x2 + 2x – 5 for values of x from x = -4 to x = 2
inclusive, that is, for -4 < x < 2.
1) Make a Table
x y = x2 + 2x – 5
-4 ( )2 + 2( ) – 5 =
-3 ( )2 + 2( ) – 5 =
-2
-1
0
1
2
y
(x, y)
( , )
( , )
2) Plot the points associated with each ordered pair (x, y).
What do you notice about the first graph as compared to the second graph?
AXIS OF SYMMETRY: x =
NOTE: The graph of a quadratic function of the
form y = ax2 + bx + c, where a, b, and c are real
numbers and a  0, is a parabola.
Does the previous parabola have symmetry and
if so, draw its line of symmetry. Write the
equation for the line of symmetry.
What if you were given the quadratic equation y
= x2 + 2x – 5 and were asked to find its axis of
symmetry without graphing the quadratic
equation. How would you do it?
How does the parabola open? Upward, like the
letter V or downward like a hill?
What is the coordinates of the turning point for
the parabola?
Is the turning point (-1, -6) considered to be a
maximum point or minimum point and why?
Before you graph the quadratic equation
y = -x2 + 2x + 5, how would you find its axis of
symmetry?
Before you graph the quadratic equation y = -x2 + 2x
+ 5, how would you find the coordinate of its turning
point?
Now graph the quadratic equation, y = -x2 + 2x + 5 for values of x
from x = -2 to x = 4 inclusive, that is, for -2 < x < 4.
1) Make a Table
x y = -x2 + 2x + 5
-2 -( )2 + 2( ) + 5 =
-1 -( )2 + 2( ) + 5 =
0
1
2
3
4
y
(x, y)
( , )
( , )
2) Plot the points associated with each ordered pair (x, y).
How does the parabola open? Upward, like the letter V or downward
like a hill?
Is the turning point (1, 6) considered to be a maximum point or
minimum point and why?
NOTE: If a is positive, the parabola opens upward and contains a minimum point.
If a is negative, the parabola opens downward and contains a maximum point.
Drill: For each of the following quadratic equations, before graphing, find their axis of symmetry, coordinates of its
turning point, and determine if the parabola opens upward and contains a minimum point or opens downward and
contains a maximum point. Then graph each quadratic equation based on its included x values.
1) y = 2x2
a=
b=
2) y = -x2 + 8x - 16
c=
a=
b=
c=
axis of symmetry is x =
axis of symmetry is x =
Coordinates of turning point:
Coordinates of turning point:
Parabola will open ____________ because a = ____
and is ____________ which means the turning point
(
,
) is a _______________ point.
Parabola will open ____________ because a = ____
and is ____________ which means the turning point
(
,
) is a _______________ point.
x
y = 2x2
y = 2( )2 =
y = 2( )2 =
y = 2( )2 =
Summary:
y
(x, y)
( , )
( , )
( , )
x
y = -x2 + 8x - 16
-( )2 + 8( ) - 16 =
-( )2 + 8( ) - 16 =
-( )2 + 8( ) - 16 =
y
(x, y)
( , )
( , )
( , )