Find the zero(s) for y=-0.5x^2-4x+8 Round your answer(s) to the nearest thousandths. -7.654,3.653 -8.732,2.139 D -9.657,1.657 -10.345,3.267

To find the zeros of the quadratic function $y=-0.5x^{2}-4x+8$, we need to solve the equation $-0.5x^{2}-4x+8=0$.<br /><br />We can use the quadratic formula to solve this equation. The quadratic formula is given by:<br /><br />$x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}$<br /><br />where $a$, $b$, and $c$ are the coefficients of the quadratic equation $ax^2+bx+c=0$.<br /><br />In this case, $a=-0.5$, $b=-4$, and $c=8$. Plugging these values into the quadratic formula, we get:<br /><br />$x=\frac{-(-4)\pm\sqrt{(-4)^2-4(-0.5)(8)}}{2(-0.5)}$<br /><br />Simplifying the expression inside the square root, we have:<br /><br />$x=\frac{4\pm\sqrt{16+16}}{-1}$<br /><br />$x=\frac{4\pm\sqrt{32}}{-1}$<br /><br />$x=\frac{4\pm4\sqrt{2}}{-1}$<br /><br />$x=-4\pm4\sqrt{2}$<br /><br />Therefore, the zeros of the quadratic function $y=-0.5x^{2}-4x+8$ are $x=-4+4\sqrt{2}$ and $x=-4-4\sqrt{2}$.<br /><br />Rounding these values to the nearest thousandths, we get:<br /><br />$x\approx-0.585$ and $x\approx-7.415$<br /><br />So, the correct answer is $-7.654,3.653$.