What is the vertex of #y= -5x^2 − 3x #?

This parabola's vertex is its maximum, so find it and set the derivative to zero:

To find the vertex of the quadratic function ( y = -5x^2 - 3x ), you can use the formula for the x-coordinate of the vertex, which is given by ( x = \frac{-b}{2a} ), where ( a ) and ( b ) are the coefficients of the quadratic function.

For the given function ( y = -5x^2 - 3x ):

• ( a = -5 )
• ( b = -3 )

Substitute these values into the formula to find the x-coordinate of the vertex: [ x = \frac{-(-3)}{2(-5)} = \frac{3}{10} ]

Once you have the x-coordinate, substitute it back into the original function to find the y-coordinate: [ y = -5\left(\frac{3}{10}\right)^2 - 3\left(\frac{3}{10}\right) ] [ y = -5 \times \frac{9}{100} - 3 \times \frac{3}{10} ] [ y = -\frac{9}{20} - \frac{9}{10} = -\frac{9}{20} - \frac{18}{20} = -\frac{27}{20} ]

So, the vertex of the function ( y = -5x^2 - 3x ) is ( \left(\frac{3}{10}, -\frac{27}{20}\right) ).