Questions: y=x+3-2

Transcript text: $y=|x+3|-2$

Solution

Solution Steps

Step 1: Identify the vertex

The given equation is in the form $y = a|x-h| + k$, where $(h, k)$ is the vertex of the absolute value graph. In this case, $h = -3$ and $k = -2$, so the vertex is at $(-3, -2)$.

Step 2: Determine the slope

The value of $a$ determines the slope of the two lines that form the absolute value graph. Since $a = 1$, the slope of the line to the right of the vertex is 1, and the slope of the line to the left of the vertex is -1.

Step 3: Plot the vertex and draw the lines

Plot the vertex $(-3, -2)$ on the graph. From the vertex, draw a line with a slope of 1 to the right. This means for every 1 unit moved to the right along the x-axis, move 1 unit up along the y-axis. From the vertex, draw a line with a slope of -1 to the left. This means for every 1 unit moved to the left along the x-axis, move 1 unit up along the y-axis.

Final Answer

The graph of $y = |x+3| - 2$ is a V-shaped graph with its vertex at $(-3, -2)$, opening upwards, and having slopes of 1 and -1 on the right and left sides of the vertex, respectively. The graph matches the given image. $ \boxed{y = |x+3|-2} $

Was this solution helpful?

Unhelpful

Helpful

Questions asked by other users

Next >