Equations don't really have x intercepts, functions or curves do. They're also known as the zeros of the function. When we set a function equal to zero we get an equation to solve, and the zeros of the function become the solutions or roots of the equation.
If a quadratic equation only has one root, that's a repeated root corresponding to a discriminant of zero.
In this example our equation is something like [tex]2(x+3)^2=0[/tex], or expanded
[tex]2x^2+12x + 18 = 0[/tex]
The discriminant [tex]d=b^2-4ac[/tex] here is
[tex] d = 12^2 - 4(2)(18) = 0 \quad\checkmark [/tex]
