Question

which equation best matches the graph shown below?
answer
\\( y = -0.2(x - 4)^2 + 3 \\) \\( y = -0.2(x + 4)^2 + 3 \\)
\\( y = -0.2(x + 4)^2 - 3 \\) \\( y = -0.2(x - 4)^2 - 3 \\)

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

From the graph, the vertex (the highest point of the parabola) is at \((4, 3)\). So \( h = 4 \) and \( k = 3 \).

Step3: Determine the Sign of \( a \)

The parabola opens downward, so \( a \) should be negative. Here, \( a = -0.2 \), which is negative.

Step4: Substitute \( h \), \( k \), and \( a \) into Vertex Form

Substituting \( h = 4 \), \( k = 3 \), and \( a = -0.2 \) into \( y = a(x - h)^2 + k \), we get \( y = -0.2(x - 4)^2 + 3 \).

Answer:

\( y = -0.2(x - 4)^2 + 3 \)