Answer: Describe the graph of y = -|x + 4| - 5.
Explanation:
AI-generated answer
The graph of the equation y = -|x + 4| - 5 is a downward-opening V-shape. The graph is a reflection of the absolute value function y = |x + 4| across the x-axis and shifted down 5 units.
Let's break down the steps to understand how the graph is formed:
1. Start with the absolute value function y = |x + 4|, which is a V-shape with the vertex at (-4, 0). This means that when x = -4, y = 0.
2. The negative sign in front of the absolute value function (-|x + 4|) reflects the graph across the x-axis. This flips the V-shape so that it opens downwards. The vertex of the reflected graph is also at (-4, 0).
3. The -5 at the end of the equation (-|x + 4| - 5) shifts the graph downward by 5 units. This means that every y-value on the graph is decreased by 5.
Overall, the graph is a downward-opening V-shape with the vertex at (-4, -5). The graph will approach negative infinity as x approaches negative infinity, and it will approach -5 as x approaches positive or negative infinity.
Example:
Let's plug in some x-values to find corresponding y-values:
When x = -6:
y = -|(-6) + 4| - 5
y = -|(-2)| - 5
y = -2 - 5
y = -7
So, when x = -6, y = -7.
When x = -2:
y = -|(-2) + 4| - 5
y = -|2| - 5
y = -2 - 5
y = -7
So, when x = -2, y = -7.
You can continue plugging in other x-values to find their corresponding y-values and plot the points to draw the graph of y = -|x + 4| - 5.