You can solve for y by turning the equation y = 2x^2 - 1 into y - intercept form
Step 1: Simplify equation
y = 2x^2 - 1 also equals y = (2^2)(x) - 1
Step 2: Simplify the equation y = (2^2)(x) - 1, to be y - intercept
y = (2^2)(x) - 1 is simplified to y = 4x - 1
Step 3: Graph y-intercept y = 4x - 1
To graph, you just need to know that the slope is m = 4 and b = -1
(I put the graph in the image below)