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Taylor fires a toy rocket from ground level. The height of the rocket with respect to time can be represented by quadratic function. If the toy rocket reaches a maximum height of 34 feet, 3 seconds after it was fired, which of the following functions could represent the height, h, of the rocket t seconds after it was fired?


A) h(t)=-16(t-3)²+34

B) h(t)=-16(t+3)²+34

C) h(t)=16(t-3)²+34

D) h(t)=16(t+3)²+34

Respuesta :

jacob193

Answer:

The function in choice

A) [tex]h(t) = -16(t - 3)^{2} + 34[/tex]

could possibly represent this relationship.

Step-by-step explanation:

Consider the vertex form of parabolas with a local extrema at [tex](x_{0}, y_{0})[/tex].

[tex]y = a(x - x_{0})^{2} + y_0[/tex].

Note the minus sign in front of [tex]x_0[/tex] in this expression.

The coefficient [tex]a[/tex] cannot be zero. The value of [tex]a[/tex] depends on the direction and width of the parabola's opening:

  • [tex]a > 0[/tex] if the parabola opens upwards, and
  • [tex]a < 0[/tex] if the parabola opens downwards.
  • The width of the opening decreases as the value of [tex]a[/tex] increases.

For this parabola,

  • [tex]a < 0[/tex] since the parabola opens downwards: the height of the rocket will eventually decrease as the rocket falls back to the ground;
  • [tex]t_0 = 3[/tex], and
  • [tex]h_0 = 34[/tex].

Among the four functions, only the function in A) meets the requirements.

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