Question

which equation best matches the graph shown below?
answer
\\( y = 0.4(x + 2)^2 - 6 \\)
\\( y = 0.4(x + 2)^2 + 6 \\)
\\( y = 0.4(x - 2)^2 + 6 \\)
\\( y = 0.4(x - 2)^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 of the parabola.

Step2: Identify the vertex from the graph

Looking at the graph, the vertex (the minimum point of the parabola) is at \((2, -6)\). So \( h = 2 \) and \( k = -6 \).

Step3: Substitute h and k into vertex form

Substituting \( h = 2 \) and \( k = -6 \) into the vertex form \( y = a(x - h)^2 + k \), we get \( y = a(x - 2)^2 - 6 \). From the options, the coefficient \( a = 0.4 \), so the equation is \( y = 0.4(x - 2)^2 - 6 \).

Answer:

\( y = 0.4(x - 2)^2 - 6 \) (the last option among the given choices)