Fireworks are launched into the air. The quadratic function y=-16x^2+195x+4 models the fireworks" height, y.in feet, x seconds after they are launched When should the fireworks explode so that they go off at the greatest height? What is that height? (Round answers the nearest hundredth.) A. 4.00sec,195.00t B. 720.00sec,4.00t C. 6.09sec,598.14ft D. -6.09sec,590.14ft

To find when the fireworks should explode so that they go off at the greatest height, we need to find the vertex of the quadratic function $y=-16x^{2}+195x+4$. The x-coordinate of the vertex of a quadratic function in the form $y=ax^2+bx+c$ is given by $-\frac{b}{2a}$. <br /><br />In this case, $a=-16$ and $b=195$, so the x-coordinate of the vertex is $-\frac{195}{2(-16)}=\frac{195}{32}\approx6.09$ seconds. <br /><br />To find the height at this time, we substitute $x=\frac{195}{32}$ into the original equation: <br /><br />$y=-16(\frac{195}{32})^2+195(\frac{195}{32})+4\approx598.14$ feet. <br /><br />Therefore, the fireworks should explode approximately 6.09 seconds after they are launched, and the greatest height they will reach is approximately 598.14 feet. <br /><br />So, the correct answer is C. $6.09sec,598.14ft$.