which equation has a graph that lies entirely above the x - axis?\no y=-(x + 7)^2+7\no y=(x - 7)^2-7\no y=(x…

Explanation:

Step1: Recall vertex - form of a parabola

The vertex - form of a parabola is $y=a(x - h)^2+k$, where $(h,k)$ is the vertex of the parabola. If $a>0$, the parabola opens upward, and if $a < 0$, the parabola opens downward.

Step2: Analyze each option

Option 1: $y=-(x + 7)^2+7$

Here $a=-1<0$, so the parabola opens downward. It will cross or go below the $x$ - axis.

Option 2: $y=(x - 7)^2-7$

The vertex is $(7,-7)$. Since the vertex has a $y$ - coordinate of $-7<0$ and the parabola opens upward ($a = 1>0$), the graph will cross the $x$ - axis.

Option 3: $y=(x - 7)^2+7$

The vertex is $(7,7)$. Since $a = 1>0$ (the parabola opens upward) and the $y$ - coordinate of the vertex $k = 7>0$, the entire graph of the parabola lies above the $x$ - axis.

Option 4: $y=(x - 7)^2$

The vertex is $(7,0)$. The parabola touches the $x$ - axis at the point $(7,0)$ and does not lie entirely above the $x$ - axis.

Answer:

$y=(x - 7)^2+7$