What is the vertex of y=-2x^2+10x+1 and is it a minimum or maximum

Step-by-step explanation:

it is maximum.

when leading coefficient of x² is negative,

It is downward parabola.

or

y=-2x²+10x+1

=-2 (x²-5x + (-5/2) ² - (-5/2) ²) + 1

=-2 (x-5/2) ²+2*25/4+1

=-2 (x-5/2) ²+25/2+1

=-2 (x-5/2) ²+27/2

maximum value of y is 27/2 and is attained at x=5/2

vertex is (5/2,27/2)