Explicação passo a passo:

[tex]f(x)=2x^2-1\\\\f(0)=-1\implies\text{Corta eixo y em -1}\\\\0 = 2x^2-1\implies 2x^2=1\implies x^2=\dfrac{1}{2} \implies x=\pm \sqrt{\dfrac{1}{2}}\\\\ \implies \text{Corta x em 0.707 e -0.707}\\\\\implies \text{Concavidade virada para cima, pois $a > 0$}\\\\x_v = \dfrac{-b}{2a} \implies \text{b \'e igual a 0, ent\~ao x do v\'ertice \'e 0}\\\\y_v=\dfrac{-\Delta}{4a}\implies \dfrac{-b^2+4ac}{4a} \implies \text{b \'e igual a 0, ent\~ao y do v\'ertice \'e c}\implies -1\\\\[/tex]