What would the functions

480-8t-0.8t^2
254+0.78t
look like?
How would they look like if they were added? (480+8t-0.8t^2+254+0.78t)

To visualize the functions, we can plot their graphs on a coordinate plane. The first function, 480-8t-0.8t^2, is a quadratic function, while the second function, 254+0.78t, represents a linear function. Let's break down the steps to plot these functions:

1. Plotting 480-8t-0.8t^2:
- The function is a quadratic function represented by a downward-opening parabola.
- To plot it, you can choose various values of t and substitute them into the function to get the corresponding y-values.
- Once you have a few points, you can mark them on the coordinate plane and connect them smoothly to form the graph of the quadratic function.

2. Plotting 254+0.78t:
- This function is a linear function represented by a straight line.
- Similar to the previous step, choose different values of t and substitute them into the function to obtain the corresponding y-values.
- Mark these points on the coordinate plane and connect them to form a straight line.

Now let's move on to the sum of these two functions, 480+8t-0.8t^2+254+0.78t:

To plot the sum, you will first need to simplify the expression by combining like terms:
480 + 8t - 0.8t^2 + 254 + 0.78t
= (480 + 254) + (8t + 0.78t) - 0.8t^2
= 734 + 8.78t - 0.8t^2

Now you have a simplified expression. To graph it:
- Use the same steps as explained earlier to plot a quadratic function. Use different values of t to calculate the corresponding y-values.
- Mark these points on the coordinate plane and connect them smoothly to form the graph of the quadratic function.

Keep in mind that the graph of 480+8t-0.8t^2+254+0.78t will have similar characteristics to the graph of the quadratic function 480-8t-0.8t^2, but it will also be affected by the linear function 254+0.78t.