Which equation best represents the graph shown below? Explain in detail how you

Question

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

Answer 1

y is equal to negative open paren x minus 2 close paren squared minus 3

To determine which equation best represents the graph, we need to analyze the key features of the graph.

1. The graph is a parabola. This tells us that the equation will be of the form y = a(x-h)^2 + k, where (h, k) represents the vertex of the parabola.

2. The vertex of the parabola is at the point (-2, -3). This means that the equation should have (x+2) and (x-2) terms to account for the horizontal shift.

3. The graph opens downwards, indicating a negative leading coefficient. This means that the equation should have a negative sign in front of the (x-2) term.

Taking these key features into consideration, the equation that best represents the graph is y = -(x-2)^2 - 3. This equation includes the necessary transformations: a horizontal shift to the left by 2 units (x-2) and a reflection over the x-axis (negative sign).