The height h of a thrown object as a function of horizontal distance d that it has traveled is a quadratic function. an object is thrown from ground level, 57 m away from the base of a tower 17 m high and just barely clears the top of the tower. it then lands 57 m away on the other side. find h(d), the quadratic function that represents this.

  h(d) = (17/3249)(-d² +114d)

Step-by-step explanation:

For this purpose, it is convenient to translate and scale a quadratic parent function so it has the desired characteristics. We can start with the function ...

  f(x) = 1 -x² . . . . . . . has zeros at x = ±1 and a vertex at (0, 1)

We want to horizontally expand this function by a factor of 57, so we can replace x by x/57. We want to vertically scale it by a factor of 17, so the vertex is at (0, 17). Finally, we want to translate the function 57 m to the right, which requires replacing x with x-57. After these transformations, we have ...

  f(x) = 17(1 -((x-57)/57)²) = (17/3249)(-x²+114x)

Using the appropriate function name and variable, we have ...

  h(d) = (17/3249)(-d² +114d)

first anwser choice.

step-by-step explanation:

the greater/less or equal to symbol (> or < with the line at the bottom) is a closed/filled in circle.

-5c + 2 _< _27

subtract from both sides by 2

-5c _< _ 27

divide both sides by -5

c _< _ 5.4

flip the inequality sign

c _> _5.4

the only possible answer that would match the simplified inequality is the first answer choice