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 (highest point) is at \((4, 3)\). So \( h = 4 \) and \( k = 3 \).

Step3: Determine the sign of \( a \)

The parabola opens downward, so \( a \) is negative.

Step4: Match with the options

Looking at the options, the equation with \( h = 4 \), \( k = 3 \), and negative \( a \) is \( y = -0.2(x - 4)^2 + 3 \).

Answer:

\( y = -0.2(x - 4)^2 + 3 \) (the first option: \( y = -0.2(x - 4)^2 + 3 \))