So for this, we will have to find the zeros (x-intercepts) of the equation. In this case, we will be using the quadratic formula, which is [tex] x=\frac{-b+\sqrt{b^2-4ac}}{2a},\frac{-b-\sqrt{b^2-4ac}}{2a} [/tex] (a = x^2 coefficient, b = x coefficient, c = constant). Using our info, our equation is such: [tex] x=\frac{-3+\sqrt{3^2-4*(-16)*4}}{2*(-16)},\frac{-3-\sqrt{3^2-4*(-16)*4}}{2*(-16)} [/tex]
Firstly, solve the multiplications and the exponents: [tex] x=\frac{-3+\sqrt{9+256}}{-32},\frac{-3-\sqrt{9+256}}{-32} [/tex]
Next, do the addition: [tex] x=\frac{-3+\sqrt{265}}{-32},\frac{-3-\sqrt{265}}{-32} [/tex]
Next, plug in the equations into the calculator and your answer will be: [tex] x=-0.41,0.60 [/tex]
Since we can't have negative time in this situation, it can't be -0.41 seconds. Which means that the object is visible for about 0.60 seconds, or C.
