Answer:
[tex]y=2x^{2} -1[/tex]
Step-by-step explanation:
For a parabolic equation to NOT contain the point (0,0) it must have a numeric constant independent from both x and y variables, so the general form would be as follows:
[tex]y=2x^{2} +c[/tex]
Solving the equation for the point (1,1) would give the necessary value for the constant "c" to make the equation valid:
[tex]y=2x^{2} +c\\1=2*(1)^{2} +c\\c = 1 -2 = -1[/tex]
Therefore, the equation that meets both of the required conditions is:
[tex]y=2x^{2} -1[/tex]
