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 perform a similar example, you need to follow these steps:
1. Identify the application: Think of a real-life situation that can be represented by a quadratic function. In this case, the example provided is about a ball being thrown into the air from a building.
2. Write the equation of the quadratic function: The equation for the height of the ball, S, at time t is given as S(t) = -16t^2 + 32t + 50. This equation represents the ball's vertical motion.
3. Determine the meaning of x and y in the application: In this case, t represents time in seconds, and S represents the height of the ball in feet.
4. Choose values for t: Select at least two values for t to input into the function. For simplicity, let's choose t = 3 and t = 4.
5. Calculate the corresponding y values: Substitute each value of t into the equation and solve for S (the height of the ball).
- For t = 3: S(3) = -16(3)^2 + 32(3) + 50 = 14. After 3 seconds, the height of the ball is 14 feet.
- For t = 4: S(4) = -16(4)^2 + 32(4) + 50 = 66. After 4 seconds, the height of the ball is 66 feet.
6. Interpret the results: In terms of the real-life application, the value of t represents the time in seconds since the ball was thrown, and the value of S represents the height of the ball above the ground in feet. So, when t = 3, it means that 3 seconds after the ball was thrown, it is 14 feet above the ground. Similarly, when t = 4, it means that 4 seconds after the ball was thrown, it is 66 feet above the ground.
Remember to properly reference any sources, using APA style, that provide the equation or information for your real-life example.