Question

which equation best matches the graph shown below?
answer
\\( y = -0.5(x - 1)^2 + 2 \\)
\\( y = 0.5(x - 1)^2 + 2 \\)
\\( y = 0.5(x + 1)^2 + 2 \\)
\\( y = -0.5(x + 1)^2 + 2 \\)

Explanation:

Step1: Analyze the parabola's direction

The parabola opens downward, so the coefficient of the squared term should be negative. This eliminates the options with positive coefficients (\(y = 0.5(x - 1)^2 + 2\) and \(y = 0.5(x + 1)^2 + 2\)).

Step2: Find the vertex form

The vertex form of a parabola is \(y = a(x - h)^2 + k\), where \((h, k)\) is the vertex. The vertex of the graph is at \((1, 2)\), so \(h = 1\) and \(k = 2\). Substituting into the vertex form with a negative coefficient (from Step 1), we get \(y = -0.5(x - 1)^2 + 2\).

Answer:

\(y = -0.5(x - 1)^2 + 2\)