Questions: Find the correct graph of the equation. y=-(x+2)^2-4 Choose the correct graph on the right.

Solution Steps

To find the correct graph of the equation \( y = -(x+2)^2 - 4 \), we need to understand the transformation of the basic parabola \( y = x^2 \). The equation involves a horizontal shift, a vertical shift, and a reflection. Specifically, the graph is shifted 2 units to the left, 4 units down, and is reflected over the x-axis. We can plot this equation to visualize the graph.

To solve the problem of finding the correct graph of the equation \( y = -(x+2)^2 - 4 \), we will analyze the equation step by step.

The given equation is a quadratic equation in the form of a parabola. The general form of a parabola is \( y = a(x-h)^2 + k \), where \((h, k)\) is the vertex of the parabola.

The equation \( y = -(x+2)^2 - 4 \) can be rewritten in the vertex form:

• The term \((x+2)\) indicates a horizontal shift to the left by 2 units.
• The constant \(-4\) indicates a vertical shift downward by 4 units.

Thus, the vertex of the parabola is \((-2, -4)\).

The coefficient of the \((x+2)^2\) term is \(-1\), which is negative. This means the parabola opens downwards.

Based on the analysis:

• The vertex is at \((-2, -4)\).
• The parabola opens downwards.

The graph should show a parabola with its vertex at \((-2, -4)\) and opening downwards.

Final Answer