Question

which equation best matches the graph shown below?
answer
\\( y = 0.2(x - 3)^2 + 6 \\)
\\( y = 0.2(x + 3)^2 + 6 \\)
\\( y = 0.2(x + 3)^2 - 6 \\)
\\( y = 0.2(x - 3)^2 - 6 \\)

Explanation:

Step1: Recall vertex form of parabola

The vertex form of a parabola is \( y = a(x - h)^2 + k \), where \((h, k)\) is the vertex.

Step2: Identify the vertex from the graph

Looking at the graph, the vertex (the minimum point) is at \((-3, -6)\). So \( h = -3 \) and \( k = -6 \).

Step3: Substitute h and k into vertex form

Substituting \( h = -3 \) and \( k = -6 \) into \( y = a(x - h)^2 + k \), we get \( y = a(x - (-3))^2 + (-6) = a(x + 3)^2 - 6 \). The coefficient \( a = 0.2 \) as given in the options. So the equation is \( y = 0.2(x + 3)^2 - 6 \).

Answer:

\( y = 0.2(x + 3)^2 - 6 \) (the option: \( y = 0.2(x + 3)^2 - 6 \))