Question

Match the equations to the graphs. (Watch the increments on the x & y axis!)(3 points) Put responses in the correct input to answer the question. Select a response, navigate to the desired input and insert the response. Responses can be selected and inserted using the space bar, enter key, left mouse button or touchpad. Responses can also be moved by dragging with a mouse. y=2(x−4)2−8y=2(x−4)2−8y= 12(x−4)2−8y= 12(x−4)2−8y=(x−4)2−4y=(x−4)2−4

Answer 1

To match the given equations to their corresponding graphs, you need to analyze the structure of each equation.

1. **y = 2(x−4)² − 8**: This is a parabola that opens upwards with a vertex at (4, -8) and a vertical stretch factor of 2.

2. **y = 12(x−4)² − 8**: This is also a parabola that opens upwards with a vertex at (4, -8). However, it has a larger vertical stretch factor of 12, making it narrower than the first parabola.

3. **y = (x−4)² − 4**: This equation describes a parabola that opens upwards with a vertex at (4, -4).

To match the equations with the graphs, consider the following:

- The parabolas with the same vertex (4, -8) can be differentiated by their vertical stretch factors (2 and 12). The one with a greater stretch appears "narrower."
- The parabola with the vertex at (4, -4) will appear higher on the y-axis compared to the other two.

After assessing the graphs, match them based on these characteristics accordingly.

If you have the graphs available, assign each equation to the corresponding graph systematically based on the vertex coordinates and the shape of the parabolas.