Explanation:
The vertex form of the equation of a parabola is given by the form:
[tex]y=a(x-h)^2+k \\ \\ \\ Where: \\ \\ a \ \text{is the leading coefficient and (h,k) the vertex of the parabola:}[/tex]
The zeroes are the x-values that touches the x-axis, that is, those x-values at which [tex]y=0[/tex]. Form the equation it's easy to know that at [tex]x=2[/tex] the output [tex]y=0[/tex] because:
[tex]y=4(x-2)^2 \\ \\ If \ x=2: \\ \\ y=4(2-2)^2 \\ \\ y=4(0)^2 \\ \\ y=0[/tex]
So the only zero occurs at [tex]x=2[/tex]
