Answer:
In summary, for a shifted graph with x-intercepts at (-8,0) and (-2,0), no horizontal or vertical shifts are needed. The graph remains centered on both the x-axis and the y-axis.
Explanation:
To obtain a shifted graph with x-intercepts at (-8,0) and (-2,0), we need to determine the horizontal and vertical shifts.
Horizontal shift:
The x-intercepts occur at -8 and -2, which means the graph crosses the x-axis at these points. In the standard form of a linear equation, the x-intercepts occur when y = 0. Therefore, we can set the equation equal to zero and solve for x:
0 = mx + b
Since the y-intercept is not given in the question, we'll assume it to be zero. The equation then becomes:
0 = mx
Solving for x, we find that the slope (m) must be zero for the graph to have x-intercepts at -8 and -2. This means there is no horizontal shift needed, as the graph remains centered on the y-axis.
Vertical shift:
The y-intercept of the shifted graph is at (0,0), which means the graph crosses the y-axis at this point. The y-intercept represents the value of y when x = 0. Therefore, there is no vertical shift needed, as the graph remains centered on the x-axis as we