Respuesta :
Considering the vertex of the quadratic equation, it is found that the scuba diver reaches maximum depth after 6 seconds.
What is the vertex of a quadratic equation?
A quadratic equation is modeled by:
[tex]y = ax^2 + bx + c[/tex]
The vertex is given by:
[tex](x_v, y_v)[/tex]
In which:
[tex]x_v = -\frac{b}{2a}[/tex]
[tex]y_v = -\frac{b^2 - 4ac}{4a}[/tex]
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 depth is given by:
D(x) = -x² + 12x + 4.
Which means that the coefficients are a = -1, b = 12, c = 4, hence:
[tex]x_v = -\frac{b}{2a} = -\frac{12}{-2} = 6[/tex]
The scuba diver reaches maximum depth after 6 seconds.
More can be learned about the vertex of a quadratic equation https://brainly.com/question/24737967
