Question

The depth in feet, D. of a scuba diver can be modeled by the function D(x) = -x + 12x + 4. where x is the number of seconds spent diving.
What is the number of seconds spent diving when the scuba diver reaches their maximum depth?
Respond in the space provided

Answer 1

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:

$y = ax^2 + bx + c$

The vertex is given by:

$(x_v, y_v)$

In which:

$x_v = -\frac{b}{2a}$

$y_v = -\frac{b^2 - 4ac}{4a}$

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:

$x_v = -\frac{b}{2a} = -\frac{12}{-2} = 6$

The scuba diver reaches maximum depth after 6 seconds.

More can be learned about the vertex of a quadratic equation brainly.com/question/24737967