Answer:
[tex]y = (x - 7)^{2} + 7[/tex].
Step-by-step explanation:
Let [tex]a[/tex], [tex]h[/tex], and [tex]k[/tex] be constants, and let [tex]a \ne 0[/tex]. The equation [tex]y = a\, (x - h)^{2} + k[/tex] represents a parabola in a plane with vertex at [tex](h,\, k)[/tex].
For example, for [tex]y = -(x + 7)^{2} + 7 = -(x - (-7))^{2} + 7[/tex], [tex]a = (-1)[/tex], [tex]h = (-7)[/tex], and [tex]k = 7[/tex].
A parabola is entirely above the [tex]x[/tex]-axis only if this parabola opens upwards, with the vertex [tex](h,\, k)[/tex] above the [tex]x\![/tex]-axis.
The parabola opens upwards if and only if the leading coefficient is positive: [tex]a > 0[/tex].
For the vertex [tex](h,\, k)[/tex] to be above the [tex]x[/tex]-axis, the [tex]y[/tex]-coordinate of that point, [tex]k[/tex], must be strictly positive. Thus, [tex]k > 0[/tex].
Among the choices:
