Transcript jeopardy slides - Mr. Young`s Math Website: Moses Brown School

JEOPARDY!!!
HOSTED by Mr. Young
Moses Brown School
RULES
• Today we are playing Jeopardy to Review for our test
tomorrow.
• Get in groups of 2-3. You must all sit together.
• Each person will get a Marker and a Board.
• You will get about 30 seconds-2 minutes to answer each
question.
• The team who chose the question can get double the points
if they get the question right and hit a bball shot.
• All other teams can get the normal points for answering the
question correctly
• Only hold up your answer on your board when you are told.
• Have someone record your points on your board.
• The top 3 teams will get a prize.
JEOPARDY: Conic Sections
Parabolas
Circles/Ellipses
Hyperbolas
Grab Bag (Any
Conic Section)
100
100
100
100
200
200
200
200
300
300
300
300
400
400
400
400
Final Jeopardy
Parabolas: 100
Graph the parabola. Find the coordinates of the vertex
And the coordinates of the focus.
(x – 2)2 = 24(y + 4)
ANSWER?
Parabolas: 100
Graph the parabola. Find the coordinates of the vertex
And the coordinates of the focus.
(x – 2)2 = 24(y + 4)
Vertex: (2, -4)
Focus: (2, 2)
ANSWER?
Parabolas: 200
Write the equation of the parabola with the following
features.
a.) Focus (-4, 0) and a vertex at (-6,0)
ANSWER?
Parabolas: 200
Write the equation of the parabola with the following
features.
a.) Focus (-4, 0) and a vertex at (-6,0)
y2 = 8(x + 6)
ANSWER?
Parabolas: 300
A gyms overhead lights have a parabolic reflector that forms
a “bowl” which is 20 inches wide from rim to rim and 12
inches deep. If the filament of the light bulb is located at the
focus (so that the beams of light reflect in parallel lines
making it easier for the driver to see) how far from the vertex
of the reflector is the filament?
ANSWER?
Parabolas: 300
A gyms overhead lights have a parabolic reflector that forms
a “bowl” which is 20 inches wide from rim to rim and 12
inches deep. If the filament of the light bulb is located at the
focus (so that the beams of light reflect in parallel lines
making it easier for the driver to see) how far from the vertex
of the reflector is the filament?
2.083 inches
ANSWER?
Parabolas: 400
Find the vertex, focus, and directrix of the conic section
x2 + 12x + 3y + 9 = 0
ANSWER?
Parabolas: 400
Find the vertex, focus, and directrix of the conic section
x2 + 12x + 3y + 9 = 0
(x + 6)2 = -3(y – 9)
Vertex: (-6, 9)
Focus: (-6, 8.25)
Directrix: y = 9.75
ANSWER?
Ellipses: 100
Graph the ellipse below. Find the Foci and Vertices.
x2 + 16y2 = 64
ANSWER?
Ellipses: 100
Graph the ellipse below. Find the Foci and Vertices.
x2 + 16y2 = 64
A=8
B=2
Vertices (8, 0) and (-8, 0)
Foci: (√68, 0) and (-√68, 0)
ANSWER?
Circles: 200
Find the center and radius
x2 + y2 + 12y - 25 = 0
ANSWER?
Circles: 200
Find the center and radius
x2 + y2 + 12y - 25 = 0
Center: (0, -6)
Radius: √61
ANSWER?
Ellipses: 300
The planets move around the sun in elliptical orbits with
the sun at one focus. The point in the orbit at which the
planet is closest to the sun is called perihelion and the
point at which it is farthest is called aphelion. These
points are the vertices of the orbit. Mercury’s distance
from the sun is 46,000,000km at perihelion and
70,000,000km at aphelion. Find an equation for mercury’s
orbit (place the origin at the center of the of the
orbit with the sun on the x-axis).
ANSWER?
Ellipses: 300
The planets move around the sun in elliptical orbits with
the sun at one focus. The point in the orbit at which the
planet is closest to the sun is called perihelion and the
point at which it is farthest is called aphelion. These
points are the vertices of the orbit. Mercury’s distance
from the sun is 46,000,000km at perihelion and
70,000,000km at aphelion. Find an equation for mercury’s
orbit (place the origin at the center of the of the
orbit with the sun on the x-axis).
x2
y2
+
=1
15
15
3.364 ´10
3.22 ´10
ANSWER?
Circles: 400
Find the solution to the system of equations 4x + 2y = 10 and
(x+2)2 + (y – 5)2 = 121 . Find the coordinates of intersection
algebraically.
ANSWER?
Circles: 400
Find the solution to the system of equations 4x + 2y = 10 and
(x+2)2 + (y – 5)2 = 121 . Find the coordinates of intersection
algebraically.
Solutions:
(-5.25, 15.51)
(4.45, -3.91)
ANSWER?
Hyperbolas: 100
Find an equation for the hyperbola that satisfies the condition.
a.) Focus at (+/-5, 0), Vertices ((+/-4, 0)
ANSWER?
Hyperbolas: 100
Find an equation for the hyperbola that satisfies the condition.
a.) Focus at (+/-5, 0), Vertices ((+/-4, 0)
x 2 y2
- =1
16 9
ANSWER?
Hyperbolas: 200
Sketch a graph the hyperbola.
Include the center, central box
and asymptotes.
(x + 2) (y + 3)
=1
16
9
2
2
ANSWER?
Hyperbolas: 200
Graph the hyperbola. Include the center,
central box and equation of the
asymptotes.
(x + 2) (y + 3)
=1
16
9
2
2
Center: (-2, -3)
A=4
B=3
Asymptotes: y = 3/4x – 1.5
y = -3/4x – 4.5
ANSWER?
Hyperbolas: 300
Find the center, foci, vertices and asymptotes.
-9x2 + 16y2 – 64y - 80 = 0
ANSWER?
Hyperbolas: 300
Find the center, foci, vertices and asymptotes.
-9x2 + 16y2 – 64y - 80 = 0
Center: (0, 2)
Vertices: (0, 5) and (0, -1)
Foci: (0, 7) and (0, -3)
Asymptotes: y = 3/4x + 2 and y = -3/4x + 2
ANSWER?
Hyperbolas: 400
The figure below shows the path of a comet in hyperbolic
motion. Find an equation for the path of the comet
assuming that the closest that the comet comes to the
earth is 20,000 miles and that the path the comet was
taking before it neared the solar system is a at a right
angle to the path it continues after leaving the solar
system.
Draw in the figure.
ANSWER?
Hyperbolas: 400
The figure below shows the path of a comet. Find an
equation for the path of the comet assuming that the
closest that the comet comes to the earth is 20,000 miles
and that the path the comet was taking before it neared
the solar system is a at a right angle to the path it
continues after leaving the solar system.
x2
y2
=1
2331370850 2331370850
ANSWER?
Grab Bag: 100
SAT QUESTION
ANSWER?
Grab Bag: 100
SAT QUESTION
ANSWER?
Grab Bag: 200
Find the equation of the circle.
The center is (-2, 5) and the circle is tangent to the line y = 9.
ANSWER?
Grab Bag: 200
Find the equation of the circle.
The center is (-2, 5) and the circle is tangent to the line y = 9.
(x+2)2 + (y – 5)2 = 16
ANSWER?
Grab Bag: 300
Graph the Conic Section. Include important aspects.
4x2 + y2 = 4y + 12
ANSWER?
Grab Bag: 300
Graph the Conic Section. Include important aspects
(center, vertices, foci).
2
2
4x2
+
y2
= 4y + 12
Ellipse.
A= 4
B=2
Oriented on y axis
x (y - 2)
+
=1
4
16
Center: (0, 2)
Vertices: (0, 6) and (0, -2)
Foci: (0, 2+√12) and (0, 2-√12)
ANSWER?
Grab Bag: 400
The circle is tangent to the line x = -2 and has x-intercepts
at -1 and 7.
Find where this circle intersects the line y = 2x - 4
ANSWER?
Grab Bag: 400
The circle is tangent to the line x = -2 and has x-intercepts
at -1 and 7.
Find where this circle intersects the line y = 2x - 4
ANSWER?
FINAL JEOPARDY !!!!
1.Graph the following Function on the graph and its inverse?
F(x) = 2x + 3
2. How are the function and the inverse related?
ANSWER?
FINAL JEOPARDY !!!!
1.Graph the following Function on the graph and its inverse?
F(x) = 2x + 3
2. How are the function and the inverse related?
The graph is reflected over y = x.
ANSWER?