Considering the vertex of the quadratic function, it is found that:
A robot traveling along the surface of the curved pit reaches a minimum depth of -22.25 feet.
<h3>What is the vertex of a quadratic equation?</h3>
A quadratic equation is modeled by:
![y = ax^2 + bx + c](https://tex.z-dn.net/?f=y%20%3D%20ax%5E2%20%2B%20bx%20%2B%20c)
The vertex is given by:
![(x_v, y_v)](https://tex.z-dn.net/?f=%28x_v%2C%20y_v%29)
In which:
Considering the coefficient a, we have that:
- If a < 0, the vertex is a maximum point.
- If a > 0, the vertex is a minimum point.
In this problem, the function is given by:
y = 0.75x² - 13.5x + 57.75.
Which means that the coefficients are a = 0.75 > 0, b = -13.5, c = 57.75.
Thus, the minimum value is given by:
![y_v = -\frac{(-13.5)^2 - 4(0.5)(57.75)}{4(0.75)} = -22.25](https://tex.z-dn.net/?f=y_v%20%3D%20-%5Cfrac%7B%28-13.5%29%5E2%20-%204%280.5%29%2857.75%29%7D%7B4%280.75%29%7D%20%3D%20-22.25)
Thus:
A robot traveling along the surface of the curved pit reaches a minimum depth of -22.25 feet.
More can be learned about the vertex of a quadratic function at brainly.com/question/24737967