y=-0.1458333333x²+0.0416666667x+13.5

y=-0.1458333333(x-0.1426611797)²+13.5

This is the St. Louis Arch, also called the Gateway Arch or the Gateway to the West, is the main attraction of the Jefferson National Expansion Memorial in St. Louis, Missouri. It’s construction started in February 12, 1963, and was finished in October 28, 1965. The Gateway Arch weighs 17,246 pounds and used 900 tons of stainless steel. I chose it because it was the first thing that popped into my head when I though of parabolas in real life, and I thought I it would be interesting to find the equation of  one of USA’s famous monuments.

(-4, 11), (0, 13.5), (2, 13), (-6, 8), (6, 8.5), (12, -7), (14, -14.5), (18, -33), (-10, -1.5), (-12, -8)

 

This graph I used the three points (0, 13.5), (2, 13), (12, -7) for the points. I made a matrix of it (0, 0, 1, 13.5), (4, 2, 1, 13), (144, 12, 1, -7) and used the rref function on my graphing calculator and got a=-0.1458333333, b=0.0416666667, and c=13.5. I plugged those numbers into my graphing to graph the line into there and then compared whether or not they looked alike. Satisfied, I went and plugged the equation into Holt’s Graphing Calculator to find the points on the line.

This is the bottom view of the Eiffel Tower. Located in Paris, France, the construction was started in January 28, 1887, and was finished in March 31, 1889. The Eiffel Tower uses 7.5 kilowatts of electricity annually to light up the tower at night. I chose the Eiffel Tower because not many people think of parabolas when they see the Eiffel Tower. Most people see the pyramid-like shape, but when I searched up “parabolas in real life”, this picture showed up, so I though it would be pretty creative to find the equation of the parabola of the Eiffel Tower.

 

y=-0.0625x²+2

y=-0.0625x²+2

 

(0, 2), (4, 1), (-4, 1), (8, -2), (-8, -2), (12, -7), (-12, -7)

 

I found out the equation of this graph by using the three points (0, 2), (4, 1), and (8, -2). I put the numbers into a matrix ( 0, 0, 1, 2) (16, 4, 1, 1) (64, 8, 1, -2) and I used rref on my graphing calculator to find that a=-0.0625, b=0, and c=2. I plugged those numbers into my graphing to graph the line into there and then compared whether or not they looked alike. Satisfied, I went and plugged the equation into Holt’s Graphing Calculator to find the points on the line.