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+34B) h(t)=-16(t+3)²+34C) h(t)=16(t-3)²+34D) h(t)=16(t+3)²+34

Answer:The function in choiceA) [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.