Question

graph the function $f(x) = -7(x + 2)^2 - 1$. plot the vertex. then plot another point on the parabola. if you make a mistake, you can erase your parabola by selecting the second point and placing it on top of the first.

Explanation:

Step1: Identify the vertex form

The function is given in vertex form \( f(x) = a(x - h)^2 + k \), where \((h, k)\) is the vertex. For \( f(x) = -7(x + 2)^2 - 1 \), we rewrite \( x + 2 \) as \( x - (-2) \), so \( h = -2 \) and \( k = -1 \). Thus, the vertex is \((-2, -1)\).

Step2: Find another point

Let's choose \( x = -1 \) (a value close to the vertex for simplicity). Substitute \( x = -1 \) into the function:
\( f(-1) = -7(-1 + 2)^2 - 1 = -7(1)^2 - 1 = -7 - 1 = -8 \). So the point \((-1, -8)\) lies on the parabola. Also, since \( a = -7 < 0 \), the parabola opens downward.

Answer:

Vertex: \((-2, -1)\); Another point: \((-1, -8)\) (plot these on the graph as instructed).