Question

1. identify the quadratic equation for the graph by determining the vertex and creating a table of values.

o y=-(x + 4)^2
o y=(x + 4)(x - 4)

Explanation:

Step1: Recall vertex - form of quadratic function

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

Step2: Analyze the given functions

For \(y=(x + 4)(x - 4)=x^{2}-16\), the vertex is \((0,-16)\) and \(a = 1>0\), so it opens upward.
For \(y=-(x + 4)^{2}=-x^{2}-8x - 16\), the vertex - form is \(y=-(x-(-4))^{2}+0\), the vertex is \((-4,0)\) and \(a=-1<0\), so it opens downward.
From the graph, the parabola opens downward and the vertex is on the \(x\) - axis near \(x=-4\).

Answer:

\(y=-(x + 4)^{2}\)