Question

identify the vertex, axis of symmetry, and direction of the graph of each function. compare the width of the graph to the width of the graph of $f(x)=x^{2}$. $h(x)=-8(x + 1)^{2}-1$ the vertex is $(-1,-1)$ (type an ordered pair) the axis of symmetry is $x=-1$ (type an equation) the graph opens

Explanation:

Step1: Recall the form of a quadratic function

The vertex form of a quadratic function is \( y = a(x - h)^2 + k \), where \((h, k)\) is the vertex and the coefficient \(a\) determines the direction and width of the parabola.

Step2: Analyze the coefficient \(a\) for direction

In the function \( h(x) = -8(x + 1)^2 - 1 \), we can identify \(a=-8\). When \(a>0\), the parabola opens upward, and when \(a < 0\), the parabola opens downward. Since \(a=-8<0\), the graph opens downward.

Answer:

downward