Use the quadratic function f(x)=-5x^2+11x+6 to answer the following questions. a) Use the vertex formula to determine the vertex. The vertex is ((11)/(10),12.05) (Type an ordered pair Simplify your answer.)

To find the vertex of the quadratic function $f(x)=-5x^{2}+11x+6$, we can use the vertex formula:<br /><br />The x-coordinate of the vertex is given by $x = -\frac{b}{2a}$, where $a$ is the coefficient of $x^2$ and $b$ is the coefficient of $x$.<br /><br />In this case, $a = -5$ and $b = 11$. Plugging these values into the formula, we get:<br /><br />$x = -\frac{11}{2(-5)} = \frac{11}{10}$<br /><br />To find the y-coordinate of the vertex, we substitute the x-coordinate back into the original function:<br /><br />$f(\frac{11}{10}) = -5(\frac{11}{10})^2 + 11(\frac{11}{10}) + 6$<br /><br />Simplifying this expression, we get:<br /><br />$f(\frac{11}{10}) = -5(\frac{121}{100}) + \frac{121}{10} + 6$<br /><br />$f(\frac{11}{10}) = -\frac{605}{100} + \frac{1210}{100} + \frac{600}{100}$<br /><br />$f(\frac{11}{10}) = \frac{1205}{100} = 12.05$<br /><br />Therefore, the vertex of the quadratic function is $(\frac{11}{10}, 12.05)$.