Question

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

Explanation:

Step1: Analyze parabola direction

The graph opens downward, so the coefficient of \((x - h)^2\) should be negative. Eliminate options with positive coefficients (first two options: \(y = 0.2(x - 4)^2 + 2\) and \(y = 0.2(x + 4)^2 + 2\)).

Step2: Identify vertex form

The vertex form of a parabola is \(y = a(x - h)^2 + k\), where \((h, k)\) is the vertex. From the graph, the vertex is at \((-4, 2)\) (since it's a downward - opening parabola, \(h=-4\), \(k = 2\)).
For the third option \(y=-0.2(x + 4)^2+2\), we can rewrite \((x + 4)\) as \((x-(-4))\), so \(h=-4\), \(k = 2\), and \(a=-0.2\) (negative, correct direction).
For the fourth option \(y=-0.2(x - 4)^2+2\), \(h = 4\), which does not match the vertex's \(x\) - coordinate of \(-4\).

Answer:

\(y=-0.2(x + 4)^2 + 2\) (assuming the third option is \(y=-0.2(x + 4)^2+2\))