Question

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

Explanation:

Step1: Analyze the parabola's direction

The graph opens downward, so the coefficient of the squared term should be negative. This eliminates the options \( y = 0.2(x - 3)^2 + 3 \) and \( y = 0.2(x + 3)^2 + 3 \) since their coefficients are positive.

Step2: Find the vertex form and vertex position

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 \((-3, 3)\) (since it's shifted left 3 units and up 3 units). For the vertex \((h, k)=(-3, 3)\), the equation should have \((x + 3)\) (because \(x - (-3)=x + 3\)) and \(+ 3\). Among the remaining options (\(y=-0.2(x + 3)^2 + 3\) and \(y=-0.2(x - 3)^2 + 3\)), the one with \((x + 3)\) matches the vertex position.

Answer:

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