PARABOLAS Do Now: Questions 1-9 find the equation of each parabola and name the transformation from...
-
Upload
mavis-douglas -
Category
Documents
-
view
218 -
download
4
Transcript of PARABOLAS Do Now: Questions 1-9 find the equation of each parabola and name the transformation from...
![Page 1: PARABOLAS Do Now: Questions 1-9 find the equation of each parabola and name the transformation from x 2.](https://reader036.fdocuments.in/reader036/viewer/2022062422/56649ee85503460f94bf950c/html5/thumbnails/1.jpg)
PARABOLASPARABOLASDo Now: Questions 1-9 find the equation of each parabola and name the transformation from x2
![Page 2: PARABOLAS Do Now: Questions 1-9 find the equation of each parabola and name the transformation from x 2.](https://reader036.fdocuments.in/reader036/viewer/2022062422/56649ee85503460f94bf950c/html5/thumbnails/2.jpg)
![Page 3: PARABOLAS Do Now: Questions 1-9 find the equation of each parabola and name the transformation from x 2.](https://reader036.fdocuments.in/reader036/viewer/2022062422/56649ee85503460f94bf950c/html5/thumbnails/3.jpg)
Things to know about Things to know about parabolasparabolas
A parabola is the set of all points equidistant from a fixed line, called the Directrix, and a fixed point not on the line, called the focus.
Equation of a parabola y = a(x - h)2 + k The vertex is at point (h, k) The axis of symmetry is the line x = h The graph of y = ax2 opens upward if a > 0 and downward if a <
0. The larger the value of | a | is, the narrower the graph of the
parabola is.
![Page 4: PARABOLAS Do Now: Questions 1-9 find the equation of each parabola and name the transformation from x 2.](https://reader036.fdocuments.in/reader036/viewer/2022062422/56649ee85503460f94bf950c/html5/thumbnails/4.jpg)
TIME FOR THE HARD STUFFTIME FOR THE HARD STUFF
An object is launched at 19.6 meters per second (m/s) from a
58.8-meter tall platform. The equation for the object's height s at time t seconds after launch is
s(t) = –4.9t2 + 19.6t + 58.8, where s is in meters. When does
the object strike the ground?
![Page 5: PARABOLAS Do Now: Questions 1-9 find the equation of each parabola and name the transformation from x 2.](https://reader036.fdocuments.in/reader036/viewer/2022062422/56649ee85503460f94bf950c/html5/thumbnails/5.jpg)
STUDENT WORKSTUDENT WORK
![Page 6: PARABOLAS Do Now: Questions 1-9 find the equation of each parabola and name the transformation from x 2.](https://reader036.fdocuments.in/reader036/viewer/2022062422/56649ee85503460f94bf950c/html5/thumbnails/6.jpg)
ANSWERANSWER
0 = –4.9t2 + 19.6t + 58.8 0 = t2 – 4t – 12
0 = (t – 6)(t + 2)
The object strikes the ground six seconds after launch.
![Page 7: PARABOLAS Do Now: Questions 1-9 find the equation of each parabola and name the transformation from x 2.](https://reader036.fdocuments.in/reader036/viewer/2022062422/56649ee85503460f94bf950c/html5/thumbnails/7.jpg)
#2 #2
An object in launched directly upward at 64 feet per second (ft/s) from a platform 80 feet
high. What will be the object's maximum height? When will
it attain this height?
![Page 8: PARABOLAS Do Now: Questions 1-9 find the equation of each parabola and name the transformation from x 2.](https://reader036.fdocuments.in/reader036/viewer/2022062422/56649ee85503460f94bf950c/html5/thumbnails/8.jpg)
STUDENT WORKSTUDENT WORK
![Page 9: PARABOLAS Do Now: Questions 1-9 find the equation of each parabola and name the transformation from x 2.](https://reader036.fdocuments.in/reader036/viewer/2022062422/56649ee85503460f94bf950c/html5/thumbnails/9.jpg)
ANSWERANSWER
Equation: s(t) = –16t2 + 64t + 80
h = –b/2a = –(64)/2(–16) = –64/–32 = 2 k = s(2) = –16(2)2 + 64(2) + 80 = –16(4)
+ 128 + 80 = 208 – 64 = 144
It takes two seconds to reach the maximum height of 144 feet.
![Page 10: PARABOLAS Do Now: Questions 1-9 find the equation of each parabola and name the transformation from x 2.](https://reader036.fdocuments.in/reader036/viewer/2022062422/56649ee85503460f94bf950c/html5/thumbnails/10.jpg)
Notes On “Projectile Notes On “Projectile Problems” Problems”
s(t) represents the projectile's instantaneous height at any time t
vo represents initial velocity t represents time in seconds after the projectile is released
![Page 11: PARABOLAS Do Now: Questions 1-9 find the equation of each parabola and name the transformation from x 2.](https://reader036.fdocuments.in/reader036/viewer/2022062422/56649ee85503460f94bf950c/html5/thumbnails/11.jpg)
EXAMPLEEXAMPLE
A ball is thrown directly upward from an initial height of 200 feet with an initial
velocity of 96 feet per second. After how many seconds will the ball reach its maximum height? And, what is the
maximum height?
![Page 12: PARABOLAS Do Now: Questions 1-9 find the equation of each parabola and name the transformation from x 2.](https://reader036.fdocuments.in/reader036/viewer/2022062422/56649ee85503460f94bf950c/html5/thumbnails/12.jpg)
Pair SharePair Share
After Mrs. Dron got hit in the head with a pitch, Mr. Chester came up to bat. The equation h=-.004d2 +.96d+3 represents the path the ball took after Mr. Chester hit the first pitch. How far off the ground was the ball when it was hit by the bat?
![Page 13: PARABOLAS Do Now: Questions 1-9 find the equation of each parabola and name the transformation from x 2.](https://reader036.fdocuments.in/reader036/viewer/2022062422/56649ee85503460f94bf950c/html5/thumbnails/13.jpg)
AnswerAnswer
h=-.004d2 +.96d+3 h=-.004(0) + .96(0) + 3 h= 0 + 0 + 3 h= 3 feet, which is how far from the ground the ball was when it was hit by the bat
![Page 14: PARABOLAS Do Now: Questions 1-9 find the equation of each parabola and name the transformation from x 2.](https://reader036.fdocuments.in/reader036/viewer/2022062422/56649ee85503460f94bf950c/html5/thumbnails/14.jpg)
HomeworkHomework
Transformation Worksheet