https://padlet.com/lcross39/leiz2s54foyvt4pl Please create a Padlet post with the following: 1.) Your name, followed by the block ex: Ms. Cross, (F-block) 2.) Your Polynomial Image of higher degree (degree three or more) in nature, architecture, science, or art. The image must be your own picture. 3.) Two to three sentences of the photo caption 4.) Show at least two math concepts about the polynomial function of your image where one of which is your polynomial equation and at least one from the list: the zeros and their multiplicity, intercepts, domain and range, or increasing/decreasing intervals 5.) Post a summary of what you did in math part 6.) Give some support to your classmates' posts by "harting" them 7.) Choose at least three posts and leave a positive and constructive feedback to your classmates either on the image itself, the narrative, math, or all! en-us 2020-11-24 17:01:30 UTC 2026-03-17 17:13:50 UTC hello@padlet.com rmpietrzykowski2023 https://padlet.com/lcross39/leiz2s54foyvt4pl/wish/991744482 I took this photo in August 2017 at Lake Willoughby in Westmore, Vermont. I found it in my camera roll and thought it would be a perfect example of a polynomial for this project!]]> 2020-12-06 16:10:41 UTC https://padlet.com/lcross39/leiz2s54foyvt4pl/wish/991744482 armartinromero2023 https://padlet.com/lcross39/leiz2s54foyvt4pl/wish/991860244 I took this picture about one week ago as I was walking my dog around the Mount Holyoke Lake. It is a clear photo that shows a polynomial of a degree of three or more.

]]> 2020-12-06 17:25:04 UTC https://padlet.com/lcross39/leiz2s54foyvt4pl/wish/991860244 smanandhar2022 https://padlet.com/lcross39/leiz2s54foyvt4pl/wish/992095119 I had this photo from 2018 where I took a picture of the Himalayas from a plane window. I though the peaks of the mountains showed a polynomial of a higher degree.]]> 2020-12-06 20:08:04 UTC https://padlet.com/lcross39/leiz2s54foyvt4pl/wish/992095119 emmanzi2022 https://padlet.com/lcross39/leiz2s54foyvt4pl/wish/992248994 I chose this photo because it was taken in Nantucket which is my family’s favorite vacation spot. The dunes and hills are curved in a way that perfectly demonstrates a high degree function. ]]> 2020-12-06 22:11:31 UTC https://padlet.com/lcross39/leiz2s54foyvt4pl/wish/992248994 aehurley2022 https://padlet.com/lcross39/leiz2s54foyvt4pl/wish/992261037 I took this picture while skiing at Berkshire East, and in the background you can see multiple mountains. These mountains can demonstrate polynomials of a high degree.]]> 2020-12-06 22:23:55 UTC https://padlet.com/lcross39/leiz2s54foyvt4pl/wish/992261037 jmgauthier2022 https://padlet.com/lcross39/leiz2s54foyvt4pl/wish/992530732 This is a photo of an item from my everyday life, my glasses. The bottom and top frame of my glasses represent a higher degree polynomial function. For this project I will be using the bottom frame as the function is more distinct.]]> 2020-12-07 01:43:08 UTC https://padlet.com/lcross39/leiz2s54foyvt4pl/wish/992530732 shmcintosh2023 https://padlet.com/lcross39/leiz2s54foyvt4pl/wish/992633473 This is a picture of a deceased eastern garter snake that I took in my front yard. The flexible backbone of this small snake is a great example of a natural polynomial function of at least 4th degree.]]> 2020-12-07 02:42:54 UTC https://padlet.com/lcross39/leiz2s54foyvt4pl/wish/992633473 https://padlet.com/lcross39/leiz2s54foyvt4pl/wish/993832417 This is a picture of my cat. The shape of his ears make a 4th degree polynomial. ]]> 2020-12-07 13:12:50 UTC https://padlet.com/lcross39/leiz2s54foyvt4pl/wish/993832417 https://padlet.com/lcross39/leiz2s54foyvt4pl/wish/995009502 This is a picture I took of a sign at a corn maze I went to! The top of the sign creates a perfect 4th degree polynomial! ]]> 2020-12-07 17:17:02 UTC https://padlet.com/lcross39/leiz2s54foyvt4pl/wish/995009502 modoolittle2023 https://padlet.com/lcross39/leiz2s54foyvt4pl/wish/995087285 This is my cat Tiny in a basket. The top of the basket looks like it could fit onto the graph of a fourth degree polynomial.]]> 2020-12-07 17:32:31 UTC https://padlet.com/lcross39/leiz2s54foyvt4pl/wish/995087285 https://padlet.com/lcross39/leiz2s54foyvt4pl/wish/995771715 Jack haber f-block
This is a chain that I wear almost every day the positioning of the chain creates a higher degree polynomial function ]]> 2020-12-07 19:48:45 UTC https://padlet.com/lcross39/leiz2s54foyvt4pl/wish/995771715 https://padlet.com/lcross39/leiz2s54foyvt4pl/wish/996397034 This is a photograph of an electric guitar. The left side specifically, demonstrates a 4th degree polynomial.]]> 2020-12-07 23:43:30 UTC https://padlet.com/lcross39/leiz2s54foyvt4pl/wish/996397034 https://padlet.com/lcross39/leiz2s54foyvt4pl/wish/996405372 This is my cat griffin; he is a very fluffy example of a 3rd degree polynomial, from his head to his feet.]]> 2020-12-07 23:49:04 UTC https://padlet.com/lcross39/leiz2s54foyvt4pl/wish/996405372 https://padlet.com/lcross39/leiz2s54foyvt4pl/wish/996654749 This is a photo on the beach during a sunset that I took in Cape Cod over the summer. The clouds in the photo would represent a higher degree. ]]> 2020-12-08 02:00:53 UTC https://padlet.com/lcross39/leiz2s54foyvt4pl/wish/996654749 https://padlet.com/lcross39/leiz2s54foyvt4pl/wish/1004890578 This is a picture of a waterfall I took. The falling water represents the higher degree polynomial.]]> 2020-12-10 03:39:31 UTC https://padlet.com/lcross39/leiz2s54foyvt4pl/wish/1004890578 armartinromero2023 https://padlet.com/lcross39/leiz2s54foyvt4pl/wish/1014093387 2020-12-13 19:51:58 UTC https://padlet.com/lcross39/leiz2s54foyvt4pl/wish/1014093387 armartinromero2023 https://padlet.com/lcross39/leiz2s54foyvt4pl/wish/1014094235 With the five points I put them into the calculator stat edit enter. Then stat calc for a quartic function.  After that I made the equation show up on Y1 with vars then y vars-function. The function goes on forever at the x-axis so its neg infinity to infinity. Then the function comes up barely over 0 at the y-axis then goes on forever downward which gave me the range of neg inf -> +0.18.]]> 2020-12-13 19:52:37 UTC https://padlet.com/lcross39/leiz2s54foyvt4pl/wish/1014094235 armartinromero2023 https://padlet.com/lcross39/leiz2s54foyvt4pl/wish/1014116432 2020-12-13 20:08:16 UTC https://padlet.com/lcross39/leiz2s54foyvt4pl/wish/1014116432 https://padlet.com/lcross39/leiz2s54foyvt4pl/wish/1014154881 -(3/343)(x^3) + 3
y intercept is (0,3)
x intercept is (7,0)]]> 2020-12-13 20:37:52 UTC https://padlet.com/lcross39/leiz2s54foyvt4pl/wish/1014154881 https://padlet.com/lcross39/leiz2s54foyvt4pl/wish/1014162135 I drew a line over the water from the waterfall and drew a graph over the photo. I rotated the line to be symmetrical on the y axis. The y intercept was (0,3) which meant that there was a plus 3 shift at the end of the equation. I found the zero (7,0) by looking at the graph. I used the equation shown below to find the leading coefficient. The x intercept is (7,0) and the y intercept is (0,3) based on the graph.]]> 2020-12-13 20:43:27 UTC https://padlet.com/lcross39/leiz2s54foyvt4pl/wish/1014162135 smanandhar2022 https://padlet.com/lcross39/leiz2s54foyvt4pl/wish/1014251267 2020-12-13 21:57:56 UTC https://padlet.com/lcross39/leiz2s54foyvt4pl/wish/1014251267 smanandhar2022 https://padlet.com/lcross39/leiz2s54foyvt4pl/wish/1014253598 2020-12-13 22:00:05 UTC https://padlet.com/lcross39/leiz2s54foyvt4pl/wish/1014253598 smanandhar2022 https://padlet.com/lcross39/leiz2s54foyvt4pl/wish/1014254382 First I traced the rough outlines of the mountain into my graph. Then I got points from -10 to 10 and plug the numbers into my calculator and used the method showed on thursday to find the equation. I used the trace function of the graph to find the x and y intercepts.]]> 2020-12-13 22:00:47 UTC https://padlet.com/lcross39/leiz2s54foyvt4pl/wish/1014254382 https://padlet.com/lcross39/leiz2s54foyvt4pl/wish/1014607192 The equation and zeroes of my graph ]]> 2020-12-14 02:25:42 UTC https://padlet.com/lcross39/leiz2s54foyvt4pl/wish/1014607192 https://padlet.com/lcross39/leiz2s54foyvt4pl/wish/1014614555 After putting the chain over a graph, the end of the chain was at the point (0,-6) and the other end of the chain was at (0,6). The other zeros were at (0,2) and (0,-2). I drew a picture of the chain with those points. Using the zeroes, I created an equation however I was missing the leading coefficient. After plugging the y intercept (3,0) into the equation, I was able to figure out “a”, the leading coefficient. ]]> 2020-12-14 02:30:04 UTC https://padlet.com/lcross39/leiz2s54foyvt4pl/wish/1014614555 modoolittle2023 https://padlet.com/lcross39/leiz2s54foyvt4pl/wish/1014751147 This is the equation and intercepts--as well as a few extra points--of my graph (with a roughly traced version of the picture for reference. I can't draw cats).]]> 2020-12-14 04:05:20 UTC https://padlet.com/lcross39/leiz2s54foyvt4pl/wish/1014751147 modoolittle2023 https://padlet.com/lcross39/leiz2s54foyvt4pl/wish/1014753239 I took the picture and traced it lightly onto a graph to determine where I could make the zeros, -5.5, -1.5, 1.5, and 5.5. Then, I took those zeros, turned them into factors, and multiplied them together to get a final equation. I plugged in some x values to get other points, and I had my graph.]]> 2020-12-14 04:06:56 UTC https://padlet.com/lcross39/leiz2s54foyvt4pl/wish/1014753239 shmcintosh2023 https://padlet.com/lcross39/leiz2s54foyvt4pl/wish/1014884597 The graph, equation, intercepts, domain and range, and end behavior.]]> 2020-12-14 05:40:57 UTC https://padlet.com/lcross39/leiz2s54foyvt4pl/wish/1014884597 shmcintosh2023 https://padlet.com/lcross39/leiz2s54foyvt4pl/wish/1014926909 I started by placing the snake picture on a graph and determining the zeros and y intercept. The zeros were x=-8 (multiplicity 3) and x=5 (multiplicity 1), and the y intercept was at (0,-10). Next, I wrote out f(x)=a(x+8)^3 (x-5) and found that a=1/256 by plugging the y intercept in. I wrote out the end behavior and then drew the function on the graph. The domain was (-∞,∞), and to find the range I used calc minimum to find the absolute minimum of the polynomial, which was (1.75,-11.77), so the range was [-11.77,∞).]]> 2020-12-14 06:10:37 UTC https://padlet.com/lcross39/leiz2s54foyvt4pl/wish/1014926909 ondowen2022 https://padlet.com/lcross39/leiz2s54foyvt4pl/wish/1015974638 This is the equation, graph, domain, range, and end behavior.]]> 2020-12-14 14:18:56 UTC https://padlet.com/lcross39/leiz2s54foyvt4pl/wish/1015974638 ondowen2022 https://padlet.com/lcross39/leiz2s54foyvt4pl/wish/1015983549 I began by placing a graph over the picture of my cat and outlining the 4th degree polynomial. From the polynomial I found my zeroes (x=0.3 and x= -3.3) and y-intercept (0,4.2). Then I pulled 5 points ((-3,3.5), (-2,2.8), (-1,2.6), (-0.5, 3.5), and (0.25,3.15)) and used the method done in class on Thursday. I plugged the points into my calculator and it gave me the values of the coefficients (in decimal form). From there, I converted the decimals into fractions and wrote my equation. Using the equation and graph I found my domain (-∞,∞) and range (-∞, 4.2), as well as my end behavior (as f(x) -> -∞, x ->-∞; as f(x) -> -∞, x ->∞) . ]]> 2020-12-14 14:20:52 UTC https://padlet.com/lcross39/leiz2s54foyvt4pl/wish/1015983549 https://padlet.com/lcross39/leiz2s54foyvt4pl/wish/1016061306 Equation : f(x) = .03x^4 - .87x^2 + 3
Zeros : -5, -3, 2, 5
X-intercepts : (-5,0) (-2,0) (5,0) (2,0)
Y intercept : (0,3)
Graph: shown in image]]> 2020-12-14 14:37:01 UTC https://padlet.com/lcross39/leiz2s54foyvt4pl/wish/1016061306 https://padlet.com/lcross39/leiz2s54foyvt4pl/wish/1016103851 I began by hand drawing a graphing and then tracing the top of the sign on it.. Since the top of the sign was a fourth degree polynomial and the two curves were almost exactly identical this was easy to graph. I then used the points from my graph ((-5,0) (-2,0) (5,0) (2,0) (0,3)) to find an equation using the method taught in class via a graphing calculator. Since my coordinates were all real whole numbers my equation came out to be f(x) = .03x^4 - .87x^2 + 3 and did not need any extra conversions. I already knew my zeros and intercepts by looking at my hand drawn graph, but to ensure they are correct I checked them using the intercept option in the graphing calculator. ]]> 2020-12-14 14:45:38 UTC https://padlet.com/lcross39/leiz2s54foyvt4pl/wish/1016103851 https://padlet.com/lcross39/leiz2s54foyvt4pl/wish/1016152733 This is a sunset placed in between a mountain range. The mountains represent a fourth degree polynomial function.]]> 2020-12-14 14:55:36 UTC https://padlet.com/lcross39/leiz2s54foyvt4pl/wish/1016152733 https://padlet.com/lcross39/leiz2s54foyvt4pl/wish/1016725664 Equation= x^4-4x^3+6x^2-4x-5,
Y int: (-5,0)(2.5,0), X int: (0,-5)]]> 2020-12-14 16:44:56 UTC https://padlet.com/lcross39/leiz2s54foyvt4pl/wish/1016725664 https://padlet.com/lcross39/leiz2s54foyvt4pl/wish/1016744442 I started by tracing the mountain picture. I then found three points on the graph that were easy to plug into a graphing calculator.(-5,0)(2.5,0)(0,-5) I then plugged these numbers into a graphing calculator the same way that was explained in class. The equation came out to x^4-4x^3+6x^2-4x-5. The x and y intercepts were already found by choosing the points earlier above.]]> 2020-12-14 16:48:14 UTC https://padlet.com/lcross39/leiz2s54foyvt4pl/wish/1016744442 emmanzi2022 https://padlet.com/lcross39/leiz2s54foyvt4pl/wish/1016930412 My graph with intercepts, function, and end behavior. ]]> 2020-12-14 17:23:11 UTC https://padlet.com/lcross39/leiz2s54foyvt4pl/wish/1016930412 emmanzi2022 https://padlet.com/lcross39/leiz2s54foyvt4pl/wish/1016945974 I began by looking at the photo and tracing it on the axis´ I made. I then found the zeros which were -10,-2,2,and 4. After that, I put in the zeros and then made a partial equation which was, f(x)=a(x+10)(x+2)(x-2)(x-4).
I then found the y intercept (0,-1) and plugged it into the equation so I could find a. My equation was then 
-1=a(0+10)(0+2)(0-2)(0-4).
After that was solved, the answer I got was a=-1/160. My final equation was 
f(x)=-1/160(x+10)(x+2)(x-2)(x-4).

]]> 2020-12-14 17:26:08 UTC https://padlet.com/lcross39/leiz2s54foyvt4pl/wish/1016945974 https://padlet.com/lcross39/leiz2s54foyvt4pl/wish/1017332956 This is a photo I took of a sunset in Vermont this summer! The curve created by the mountain tops represents a function of a higher degree.

]]> 2020-12-14 18:40:56 UTC https://padlet.com/lcross39/leiz2s54foyvt4pl/wish/1017332956 jmgauthier2022 https://padlet.com/lcross39/leiz2s54foyvt4pl/wish/1017961519 Equation: .003607825x^4 + -.181139178x^2 + .2982126165

Y-int= .2982126165

Domain: (-infinity, infinity)
Range: (-1.975385, infinity)]]> 2020-12-14 21:16:53 UTC https://padlet.com/lcross39/leiz2s54foyvt4pl/wish/1017961519 rmpietrzykowski2023 https://padlet.com/lcross39/leiz2s54foyvt4pl/wish/1017963766 Equation: y=-0.004x^4-0.004x^3+0.106x^2+0.119x-0.472
x-intercepts: (-4.75, 0), (-3, 0), (1.75, 0)
y-intercepts: (0, -0.5)]]> 2020-12-14 21:17:40 UTC https://padlet.com/lcross39/leiz2s54foyvt4pl/wish/1017963766 jmgauthier2022 https://padlet.com/lcross39/leiz2s54foyvt4pl/wish/1018015734 In order to get the coordinate values of the function. I put the photo over a graph in google docs and made the photo transparent. I then plugged these coordinate values I got from the graph into the "stat", "edit:1" table on my calculator. Then I used "stat", "calc: 7" in order to get the coefficient values of the function's equation. I know the y-int is .2982126165 because that is the e value the calculator gave me. I determined that since the end behavior of the function was as x approaches infinity, f(x) approaches infinity, and as x approaches -infinity, f(x) approaches infinity; that the range had a minimum value and that the domain was all real numbers. I then used the minimum calculation on my calculator to determine that the minimum value was -1.975385.]]> 2020-12-14 21:36:50 UTC https://padlet.com/lcross39/leiz2s54foyvt4pl/wish/1018015734 rmpietrzykowski2023 https://padlet.com/lcross39/leiz2s54foyvt4pl/wish/1018121592 I started off by using a website to place a grid over my image. Then, I used the grid to find eight points along the line. I made sure that these points included all x-intercepts, y-intercepts, and local minimums and maximums. I then entered the eight data points into my graphing calculator by following the directions that were explained in class. I was able to get the equation: y=-0.004x^4-0.004x^3+0.106x^2+0.119x-0.472 by using my calculator. I then used the points that I had found before to write down my x-intercepts and y-intercepts. These were found by looking at the graph.]]> 2020-12-14 22:22:08 UTC https://padlet.com/lcross39/leiz2s54foyvt4pl/wish/1018121592 aehurley2022 https://padlet.com/lcross39/leiz2s54foyvt4pl/wish/1018340592 The graph, equation, domain/range, X & Y intercepts, and end behavior ]]> 2020-12-15 00:25:02 UTC https://padlet.com/lcross39/leiz2s54foyvt4pl/wish/1018340592 aehurley2022 https://padlet.com/lcross39/leiz2s54foyvt4pl/wish/1018343891 I first started by sketching the picture of my mountain on a piece of graph paper. The points on the graph that were easy for me to use were (-5,0), (0,7), (5,5), (10,2), and (12,0). I used the method you taught us in class to determine the equation of the polynomial. My X and Y intercepts were all visible from the graph I drew (X ints: (-5,0), (12,0). Y int: (7,0)).  ]]> 2020-12-15 00:26:40 UTC https://padlet.com/lcross39/leiz2s54foyvt4pl/wish/1018343891 rmpietrzykowski2023 https://padlet.com/lcross39/leiz2s54foyvt4pl/wish/1018654856 2020-12-15 02:54:25 UTC https://padlet.com/lcross39/leiz2s54foyvt4pl/wish/1018654856 tturibe2022 https://padlet.com/lcross39/leiz2s54foyvt4pl/wish/1018721707 The photo includes the graph, x and y intercepts, the domain and range, and the equation of the function. ]]> 2020-12-15 03:33:23 UTC https://padlet.com/lcross39/leiz2s54foyvt4pl/wish/1018721707 tturibe2022 https://padlet.com/lcross39/leiz2s54foyvt4pl/wish/1018728406 The first thing that I did was sketch a zoomed in part of my photo. I then found the x intercepts which were (-3.5,0) (-1.5,0) (1.5,0) and (3,0). The next thing I did was find the y intercept which was (0,2). I then put the intercepts into an equation which was f(x)=a(x+3.5)(x+1.5)(x-1.5)(x-3). I plugged in my y intercept of (0,2) and from this equation I found a=16/189. I then plugged that in for a and had an equation of f(x)=(16/189)(x+3.5)(x+1.5)(x-1.5)(x-3). I also found the domain and range of the function which were both (-infinity,infinity) because the x and y axis can go for as long as possible. ]]> 2020-12-15 03:37:54 UTC https://padlet.com/lcross39/leiz2s54foyvt4pl/wish/1018728406 https://padlet.com/lcross39/leiz2s54foyvt4pl/wish/1028227588 Mason Diamond ]]> 2020-12-17 15:59:20 UTC https://padlet.com/lcross39/leiz2s54foyvt4pl/wish/1028227588 https://padlet.com/lcross39/leiz2s54foyvt4pl/wish/1028242250 I traced the photo, on the line of my cat's spine at an angle, and traced that onto a graph, to get intercepts at X = -4 and at X = 0 . since the function of his spine projected onto a 2 dimensional surface is a 3rd degree polynomial function, all that had to be added to my  (x+4) was a x^2, and to make the equation negative, in order to reflect it over the horizontal x axis, making the equation f(x) = -x^3-4x^2. since this equation goes in both directions on both axes to infinity the domain and range are both, (-inf, inf) .]]> 2020-12-17 16:02:40 UTC https://padlet.com/lcross39/leiz2s54foyvt4pl/wish/1028242250 armartinromero2023 https://padlet.com/lcross39/leiz2s54foyvt4pl/wish/1034581655 Polynomial
Curved lines, the domain and range
running through nature]]> 2020-12-20 18:23:25 UTC https://padlet.com/lcross39/leiz2s54foyvt4pl/wish/1034581655 shmcintosh2023 https://padlet.com/lcross39/leiz2s54foyvt4pl/wish/1034775738 The notes of the song on the staff visually create a polynomial function.

• The polynomial is 7th degree 
• The domain and range are both all real numbers
• If the treble clef is considered 0, the first note is 1, and the second note is 2 (and so on), then the decreasing intervals would be (-∞,3) (3,6) (9,12) (14,∞) and the increasing intervals would be (6,9) (12,14) 

]]> 2020-12-20 22:07:16 UTC https://padlet.com/lcross39/leiz2s54foyvt4pl/wish/1034775738 https://padlet.com/lcross39/leiz2s54foyvt4pl/wish/1035147656 Shown here is the graph of my polynomial function, the equation, the x and y intercepts, and the domain and range. ]]> 2020-12-21 03:21:13 UTC https://padlet.com/lcross39/leiz2s54foyvt4pl/wish/1035147656 https://padlet.com/lcross39/leiz2s54foyvt4pl/wish/1035159013 I first started off by sketching the image of my guitar and then placing a grid right over it. From there I figured out the x and y intercepts. The x-intercepts were (-1, 0), (0, 0), and (1, 0). The y-intercept was (0, 0). From the intercepts I was able to write the equation: -(x-0)(x+0)(x+1)(x-1). I solved that to get the equation -x^4+x^2. The domain and range are both all real numbers, in other words, (-infinity, infinity). ]]> 2020-12-21 03:26:43 UTC https://padlet.com/lcross39/leiz2s54foyvt4pl/wish/1035159013 https://padlet.com/lcross39/leiz2s54foyvt4pl/wish/1035168212 2020-12-21 03:33:48 UTC https://padlet.com/lcross39/leiz2s54foyvt4pl/wish/1035168212 jmgauthier2022 https://padlet.com/lcross39/leiz2s54foyvt4pl/wish/1036924588 Google Slide]]> 2020-12-21 23:23:00 UTC https://padlet.com/lcross39/leiz2s54foyvt4pl/wish/1036924588