Question

which equation best matches the graph shown below?
answer
\\( y = 0.3(x - 3)^2 - 5 \\)
\\( y = 0.3(x - 3)^2 + 5 \\)
\\( y = 0.3(x + 3)^2 + 5 \\)
\\( y = 0.3(x + 3)^2 - 5 \\)

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 lowest point of the parabola) is at \((3, -5)\). So \( h = 3 \) and \( k = -5 \).

Step3: Match with the vertex form

Substituting \( h = 3 \) and \( k = -5 \) into the vertex form \( y = a(x - h)^2 + k \), we get \( y = 0.3(x - 3)^2 - 5 \) (since \( a = 0.3 \) from the options).

Answer:

\( y = 0.3(x - 3)^2 - 5 \) (the first option)