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: Determine the direction of the parabola

The graph of the parabola opens downward, so the coefficient of the squared term should be negative. This eliminates the options \( y = 0.2(x - 4)^2 + 2 \) and \( y = 0.2(x + 4)^2 + 2 \).

Step2: Find the vertex of the parabola

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 \((-4, 2)\). In the vertex form, \( h = -4 \) and \( k = 2 \), so the equation should be \( y = a(x - (-4))^2 + 2 = a(x + 4)^2 + 2 \).

Step3: Determine the coefficient \( a \)

Since the parabola opens downward, \( a \) is negative. Among the remaining options (\( y = -0.2(x + 4)^2 + 2 \) and \( y = -0.2(x - 4)^2 + 2 \)), the one with \( h = -4 \) (matching the vertex's x - coordinate) is \( y = -0.2(x + 4)^2 + 2 \).

Answer:

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