The function which is quadratic is:
[tex]y-3x^2=3(x^2+5)+1[/tex]
We know that the general equation of a quadratic function is given by:
[tex]y=ax^2+bx+c[/tex]
where a , b and c are real numbers.
1)
[tex]y-3x^2=3(x^2+5)+1[/tex]
On solving we get:
[tex]y-3x^2=3x^2+15+1\\\\\\y=3x^2+3x^2+1+15\\\\\\y=6x^2+16[/tex]
Hence, the function is quadratic.
2)
[tex]y^2-7x=2(x^2+6)+7[/tex]
It is not a quadratic equation since we have a term as : [tex]y^2[/tex]
and hence the equation will not match the general equation of the quadratic function.
3)
[tex]y-2x^2=6(x^3+5)-4[/tex]
as it has a term of [tex]x^3[/tex]
Hence, it is a equation of a cubic function.
4)
[tex]y-5x=4(x+5)+9[/tex]
On solving we get:
[tex]y=9x+29[/tex]
It does not has any term of [tex]x^2[/tex]
Hence, the equation is not a quadratic function it represent a linear function.
