Show the function y=2x^2-4x-5 is one-to-one using the definition of one-to-one.
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A function f(x) is one to one if for $\displaystyle x_1,x_2$ with $\displaystyle x_1\not = x_2$ $\displaystyle f(x_1)\not = f(x_2)$
So 0 doesn't equal 2,
And yet $\displaystyle f(0)=2(0)^2-4(0)-5=-5$
And $\displaystyle f(2)=2(2)^2-4(2)-5=8-8-5=-5$
So therefore your function is not one to one