ACT Opener:
• Find 2𝑥 𝑥 − 3𝑦 + 2𝑦 2 when x= -6 and y = 3.
a) -9
b) 54
c) 81
d) 126
e) 198
Conic Sections!
Conics Sections
• A conic section is a
curve formed by the
intersection of a
plane and a double
cone. By changing the
inclination of the
plane, you can create
a circle, a parabola,
an ellipse, or a
hyperbola.
Quick Review: Domain & Range
• What is domain and what is range?
• How are the related to x and y in an equation?
Quick Review: Domain & Range
• Find the domain and range of the following
equation:
2
2
𝑥 + 𝑦 = 25
Example 1: Graphing a Circle
• Graph the equation 𝒙𝟐 + 𝒚𝟐 = 𝟐𝟓. Describe
the graph and its lines of symmetry. Then find
the domain and range.
Example 1: Graphing a Circle
• How could we graph this using our
calculators?
• How would we have to manipulate the
equation?
• Why is there no point on the graph with an xcoordinate of 6?
Student Check:
• Graph the Equation 𝟗𝒙𝟐 + 𝟏𝟔𝒚𝟐 = 𝟏𝟒𝟒.
Describe the graph and the lines of symmetry.
Find the domain and range.
• Use your white boards.
Student Check:
• What is the shape of your graph?
• How would we manipulate the equation so
that we could graph it in the calculator?
Interpreting Graphs
• Identify the center
and intercepts of
the conic section.
Then identify the
domain and range.
Student Check:
• Identify the
center and
intercepts of the
conic section.
Then identify the
domain and
range.
Partner Practice:
• Pair up with your partner to complete the
problem set.
• Only complete the problems that have been
circled.
• You will have 15 minutes to complete.
Partner Practice:
Group 1: Justin & Tristan
Group 2: Harley & Andrea
Group 3: Kelly & Jessica
Group 4: Taylor & Brando
Group 5: Samantha & Trevor
Exit Slip:
1. The graph of which
equation of a circle
contains only the
points in the table.
X
Y
-3
0
0
±3
2. Identify the domain and
range of the following conic
section.
3
0
a) 𝑥 2 + 𝑦 2 − 4 = 0
b) 6𝑥 2 + 6𝑦 2 = 54
a) Domain: 𝑥: −4 ≤ 𝑥 ≤ 4
Range: 𝑦: −5 ≤ 𝑦 ≤ 5
b) Domain: 𝑥: −5 ≤ 𝑥 ≤ 5
Range: 𝑦: −4 ≤ 𝑦 ≤ 4