Question

The graph was exact and came with the question, I tried to redraw it as accurately as possible! : - ) If there’s anything you can distinguish/read what it says, say so and I can type it out!

Answer 1

Answer: The Blue Team's pumpkin traveled the greatest distance (16m) in comparison with the Red Team's pumpkin (9m)

Step-by-step explanation

We are asked to find the team's pumpkin that traveled the farthest.

The farthest distance of each model can be known when y = 0. From the graph, we can see that it is 16m, as the coordinate is (16, 0).

From the equation:

`h(x)=-0.5x^2+4x+5`

Using the General Quadratic Formula:

`x_(1,2)=(-b\pm√(b^2-4ac))/(2a)`

where in our case a = -0.5, b = 4 and c = 5, we can replace the values and obtain x:

`x_(1,2)=(-4\pm√(4^2-2(-0.5)(5)))/(2(-0.5))`

Simplifying:

`x_1=−1.0990`
`x_2=9.0990`

Then, the Red team's pumpkin traveled 9.0990m, which is less than the 16m the Blue team's pumpkin traveled.