Answer: The Blue Team's pumpkin traveled the greatest distance (16m) in comparison with the Red Team's pumpkin (9m)
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:
[tex]h(x)=-0.5x^2+4x+5[/tex]
Using the General Quadratic Formula:
[tex]x_{1,2}=\frac{-b\pm\sqrt{b^2-4ac}}{2a}[/tex]
where in our case a = -0.5, b = 4 and c = 5, we can replace the values and obtain x:
[tex]x_{1,2}=\frac{-4\pm\sqrt{4^2-2(-0.5)(5)}}{2(-0.5)}[/tex]
Simplifying:
[tex]x_1=−1.0990[/tex][tex]x_2=9.0990[/tex]
Then, the Red team's pumpkin traveled 9.0990m, which is less than the 16m the Blue team's pumpkin traveled.
