Respuesta :
The graph of Speedy's height in the air with time, which is based on a
quadratic function is a parabola.
- The quadratic function modelling Speedy's height is given by the option; h(t) = -16·t² + 80·t + 12
Reasons:
The given parameters are;
The height of the cannon = 12 feet
Speedy's height after 2 seconds = 108 feet
Speedy's height after 3 seconds = 108 feet
Required: To select the best representation of the quadratic modelling Speedy's height, h(t), as a function of elapsed time, t?
Solution:
The path of Speedy's motion is a parabola
From the question, we have, that the initial height, at t = 0 is the height of the cannon = 12 feet
Therefore;
The equation has a constant term of 12
Given that the time it takes Speedy to rise above 108 feet and return to 108 feet = 3 - 2 = 1 second, we have;
The maximum height occurs between the 2nd and the 3rd second.
The path of a parabola is symmetric about the maximum point, therefore;
The maximum point occur at time [tex]\displaystyle 2 \, s + \frac{3 - 2}{2} \, s = 2.5 \, s[/tex]
Therefore, the x-coordinate of the vertex is t = 2.5 s
From the general equation of a parabola, a·x² + b·x + c, the x-coordinate of the vertex is; [tex]\displaystyle \mathbf{ -\frac{b}{2 \cdot a}}[/tex]
From the given option, we have the option; h(t) = -16·t² + 80·t + 12, which has;
Constant = 12
Vertex = [tex]\displaystyle -\frac{80}{2 \times (-16) } = 2.5[/tex]
Therefore;
The best representation of Speedy's height is; h(t) = -16·t² + 80·t + 12
The possible question options are;
h(t) = 1.07·t² + 5.33·t + 101.60
h(t) = 16·t² + 80·t + 12
h(t) = -1.07·t² + 5.33·t 101.60
h(t) = -16·t² + 80·t + 12
Learn more about projectile motion here:
https://brainly.com/question/24216590
https://brainly.com/question/1912408
