Find the maximum value of the parabola y=-5x^2-2x Simplify your answer and write it as a proper fraction, improper fraction, or integer. square

To find the maximum value of the parabola $y=-5x^{2}-2x$, we need to determine the vertex of the parabola. The vertex form of a parabola is given by $y=a(x-h)^{2}+k$, where $(h,k)$ is the vertex of the parabola.<br /><br />The x-coordinate of the vertex can be found using the formula $h=-\frac{b}{2a}$, where $a$ and $b$ are the coefficients of $x^{2}$ and $x$ respectively.<br /><br />In this case, $a=-5$ and $b=-2$. Plugging these values into the formula, we get:<br /><br />$h=-\frac{-2}{2(-5)}=\frac{1}{5}$<br /><br />Now that we have the x-coordinate of the vertex, we can substitute it back into the original equation to find the y-coordinate:<br /><br />$y=-5\left(\frac{1}{5}\right)^{2}-2\left(\frac{1}{5}\right)=-5\left(\frac{1}{25}\right)-\frac{2}{5}=-\frac{1}{5}-\frac{2}{5}=-\frac{3}{5}$<br /><br />Therefore, the maximum value of the parabola $y=-5x^{2}-2x$ is $\boxed{-\frac{3}{5}}$.