Question

graph the quadratic function below.
$y = -(x + 4)^2 - 4$

Explanation:

Step1: Identify Vertex Form

The quadratic is in vertex form \( y = a(x - h)^2 + k \), here \( y = -1(x - (-4))^2 + (-4) \). So vertex is \((-4, -4)\).

Step2: Determine Direction of Opening

Since \( a = -1 < 0 \), the parabola opens downward.

Step3: Find Key Points (Optional)

• For \( x = -3 \): \( y = -(-3 + 4)^2 - 4 = -1 - 4 = -5 \), point \((-3, -5)\).
• For \( x = -5 \): \( y = -(-5 + 4)^2 - 4 = -1 - 4 = -5 \), point \((-5, -5)\).
• For \( x = -2 \): \( y = -(-2 + 4)^2 - 4 = -4 - 4 = -8 \), point \((-2, -8)\).
• For \( x = -6 \): \( y = -(-6 + 4)^2 - 4 = -4 - 4 = -8 \), point \((-6, -8)\).

Step4: Plot Vertex and Points

Plot vertex \((-4, -4)\), then symmetric points like \((-3, -5)\), \((-5, -5)\), \((-2, -8)\), \((-6, -8)\). Draw a downward - opening parabola through these points.

Answer:

The graph is a parabola with vertex at \((-4, -4)\), opening downward, passing through points like \((-3, -5)\), \((-5, -5)\), \((-2, -8)\), \((-6, -8)\) (graph construction as per steps above).