Question

Jen and her friends would like a curved pit to be included in next year’s obstacle course. they found this equation to model their suggested curved pit using a computer simulation. in the equation, y is the depth of the pit in relation to the surface of the course, and x is the horizontal distance from the left edge of the entire obstacle course. both distances are in feet. y = 0.75x^2 − 13.5x + 57.75 select the correct answer from each drop-down menu. a robot traveling along the surface of the curved pit reaches a (maximum, minimum, or contrast) depth of (-3, -9, 4, or -7) feet

Answer 1

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.

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 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:

$y_v = -\frac{(-13.5)^2 - 4(0.5)(57.75)}{4(0.75)} = -22.25$

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