Find the roots and the vertex of the quadratic on a calculator. Round all values to 3 decimal places (if necessary). \[ y=-x^{2}-10 x+35 \] Answer Attempti out of 2 Roots: \( \square \) and \( \square \) Vertex: \( \square \)
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To find the roots of the quadratic \( y = -x^2 - 10x + 35 \), you can apply the quadratic formula \( x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a} \). Here, \( a = -1 \), \( b = -10 \), and \( c = 35 \). Plugging these values into the formula gives you the roots approximately as \( x = 2.410 \) and \( x = -14.410 \). For the vertex of the quadratic, use the formula \( x = -\frac{b}{2a} \). Substituting the coefficients, you will find that the x-coordinate of the vertex is \( x = -5 \). To find the corresponding y-coordinate, substitute \( x = -5 \) back into the original equation, yielding \( y = 60 \). Therefore, the vertex is \( (-5, 60) \).