Answered

Explore Westonci.ca, the leading Q&A site where experts provide accurate and helpful answers to all your questions. Connect with a community of experts ready to provide precise solutions to your questions quickly and accurately. Our platform offers a seamless experience for finding reliable answers from a network of knowledgeable professionals.

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

Sagot :

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:

[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 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:

[tex]y_v = -\frac{(-13.5)^2 - 4(0.5)(57.75)}{4(0.75)} = -22.25[/tex]

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 https://brainly.com/question/24737967

Thanks for using our platform. We aim to provide accurate and up-to-date answers to all your queries. Come back soon. We hope this was helpful. Please come back whenever you need more information or answers to your queries. Get the answers you need at Westonci.ca. Stay informed by returning for our latest expert advice.