the graph of y = x² is the solid black graph below. which function represents the dotted graph? answer y =…

Explanation:

Step1: Analyze transformations

The parent - function is $y = x^{2}$, which is a parabola opening upwards with vertex at the origin $(0,0)$. The dotted graph is a parabola opening downwards, so there is a reflection about the $x$ - axis, which means the function has a negative sign in front of the squared term. Also, the vertex of the dotted graph is at $(0, - 5)$, which means there is a vertical shift downwards by 5 units.

Step2: Write the transformed function

The general form of a quadratic function is $y=a(x - h)^{2}+k$, where $(h,k)$ is the vertex of the parabola. After reflection about the $x$ - axis ($a=-1$) and a vertical shift down by 5 units ($k = - 5$) with no horizontal shift ($h = 0$), the function is $y=-(x)^{2}-5$.

Answer:

$y =-(x)^{2}-5$