Can someone help me do an example like this one.
State the application, give the equation of the quadratic function, and state what the x and y in the application represent. Choose at least two values of x to input into your function and find the corresponding y for each. State, in words, what each x and y means in terms of your real-life application. Please see the following example. You may use other variables besides x and y, such as t and S depicted in the following example, but you may not use that example. Be sure to reference all sources using APA style.
Typing hint: To type x-squared, use x^2. Do not use special graphs or symbols because they will not appear when pasted to the Discussion Board.
When thrown into the air from the top of a 50 ft building, a ball’s height, S, at time t can be found by S(t) = -16t^2 + 32t + 50. When t = 1, s = -16(1)^2 + 32(1) + 50 = 66. This implies that after 1 second, the height of the ball is 66 feet. When t = 2, s = -16(2)^2 + 32(2) + 50 = 50. This implies that after 2 seconds, the height of the ball is 50 feet.
I want to use roller coasters and I found out that a random one goes 50 mph and is 95 feet tall. How do I apply this to the equation.
To apply the given information about the roller coaster to the equation, we need to identify the relevant variables and values.
Let's denote the time as "t" and the height of the roller coaster as "S(t)".
From the given information, we know that the roller coaster is 95 feet tall. So, we can equate this to the height function, S(t), as follows:
95 = -16t^2 + 32t + 50
To solve this equation, we rearrange it into the standard form:
-16t^2 + 32t + 50 - 95 = 0
Simplifying further:
-16t^2 + 32t - 45 = 0
To find the values of "t" when the roller coaster is at a height of 95 feet, we can use various methods such as factoring, completing the square, or the quadratic formula.
Assuming we use the quadratic formula, which states that for an equation in the form of at^2 + bt + c = 0, the values of "t" can be found using:
t = (-b ± √(b^2 - 4ac)) / (2a)
Plugging in the values from our equation, we have:
t = (-32 ± √(32^2 - 4(-16)(-45))) / (2(-16))
Simplifying further:
t = (-32 ± √(1024 - 2880)) / (-32)
t = (-32 ± √(-1856)) / (-32)
Since the result involves the square root of a negative number, it implies that there are no real solutions for "t" in this context. Therefore, the given roller coaster does not match the trajectory described by the quadratic equation -16t^2 + 32t + 50.
It's important to note that this equation represents the motion of a ball thrown into the air, not a roller coaster. The equation can only be accurately applied to scenarios involving free-falling objects in the absence of air resistance.