determine the vertex for the function

y=2x^2+5x-3

for y = ax^2 + bx + c, the x value of the vertex is -b/(2a)
sub that x into your equation to find the y.
Another way is to complete the square.

so for yours, x = -5/4 etc.

a third way, if you know Calculus, is to find the derivative of y, set that equal to zero. Solving that for x gives you the x of the vertex, sub into the original equation to find the y.