Which equation best represents the graph shown below? Explain in detail how you
arrived at your answer by stating each of the mathematical transformations necessary
to produce the graph on your scratch work.
(1 point)
Responses
y=(x+2)2−3
y is equal to open paren x plus 2 close paren squared minus 3
y=(x−2)2−3
y is equal to open paren x minus 2 close paren squared minus 3
y=12(x+2)2−3
y is equal to 1 half times open paren x plus 2 close paren squared minus 3
y=−(x−2)2−3
The equation that best represents the graph shown is y=(x-2)²-3.
To determine this, let's analyze the graph and the transformations necessary to produce it:
1. The graph is a parabola. This suggests that the equation will contain a squared term.
2. The vertex of the parabola appears to be at (2, -3). This means that the equation will involve a transformation that shifts the vertex.
3. The vertex of the original parabola is at (0, 0). Shifting the vertex to (2, -3) involves a horizontal shift of +2 units to the right (subtracting 2 from x) and a vertical shift of -3 units downward (subtracting 3 from y).
4. Putting it all together, we can see that the equation needs to have the form y = (x-2)² - 3.
Therefore, the equation y=(x-2)²-3 best represents the graph shown.