Colorado State University Global Campus W2 Quadratic Equation Discussion

Use an outside source to search for a quadratic equation that models something from your daily life.

Solve the equation in two ways.

Hello everyone,
There is a luxury 5hr river tour in brazil that goes 25 km then back to show off some landmarks. The river has a 4 km an hour current.
. total time = 25/(x-4) + 25/(x+4) = 5 hours
5(x-4)(x+4) – 25(x+4) +25(x-4)
. 51×2-8) = 25x+100+ 25x-100
. 5(x2-8)=25x + 25x
5×2-40 = 50x
.X2-8 = 10x
Quadratic Equation – x2-10X-8-0
. a= 1, b= -10, C= -8
Solve using quadratic formula –
. X=[-(-10) + (-10)2-4*1*(-8))]/(2×1)
X = [ 10 /(100+32)]/2
. X = [ 10 + (132) ]/2
X = ( 10 + (33)/2
X = (10 + 2/(33)/2 X = (10 – 21(33))/2
• X= 5-733 or x = 5+ 733
X = -0.74 or x = 10.74
This equation has two solutions but for our problem the -0.74 doesn’t make sense so our answer is 10.74 km/h.
Solved by using a graph
y=x2-10X-8
15
-10
5
-10
-5
0
10
15
10
ophon
desmos
The method I enjoyed using the most was the quadratic formula as I felt it was a easier solve.
References –
Nancy Marcus. (2022) SOLVING QUADRATIC EQUATIONS…S.O.S MATHematics. http://www.sosmath.com/aleebra/solve/solve4/s43/543.html e
MathslsFun. (2021) Quadratic Equations… MathsIsFun.com. Quadratic Equations (mathsisfun.com
Admin. (2019) Uses of quadratic equations in daily life…. allusesof.com. Uses of quadratic equations in daily life – All Uses of
Good Morning,
The quadratic equation has many different real world applications but the one I found the most interesting was when used in athletics. Lets say that
you throw a ball into the air and have your friend catch it, but you want to give her the precise time it will take the ball to arrive (Wandrei, 2022). The
values we given are as follow: starting arm height is 3 meters, speed of throwing is 14 meters per second, and gravity reduces the speed by 5 meters
per seconda. As we setup the equation, the y-integer will represent the height of the ball at any moment and the x-integer will represent the time that
has passed.
Solving by Quadratic Formula
For the quadratic formula we just plug in the values from the quadratic equation and solve for x.
y=3+ 14 – 50; a = -5, b = 14, c=3
= -14+16
– 14V 14″ – 4x3x-5
2x-5
– 10
-14+16
T = or -0.2
= -14
-14-16
Solving by Graphing
With the quadratic equation we can easily graph this and visually see where the parabola intersects the x-axis. We can also pin point the exact time we
need our friend to catch at the arm height of 3 meters which is 2.8 seconds.
y=3+ 14.0 – 5.02
2 = -0.2, 3
15
10
-5
10
15
edit
desmos
After solving for the quadratic, I have come to find that I prefer the graphing method because with graphing calculators or graphing apps we can
pinpoint our intercepts immediately. Although, the numbers may not be very pretty it still is a very effective visual for me as a visual learner.
References
Wandrei, Kevin. (2022, February 24). Everyday Examples of Situations to Apply Quadratic Equations, sciencing.com. Retrieved from
https://sciencing.com/everyday-examples situations apply-quadratic-equations-10200.html