Question

which equation best matches the graph shown below?
answer
\\( y = -5(x - 6)^2 - 4 \\) \\( y = -5(x - 6)^2 + 4 \\)
\\( y = -5(x + 6)^2 + 4 \\) \\( y = -5(x + 6)^2 - 4 \\)

Explanation:

Step1: Identify the vertex form of a parabola

The vertex form of a parabola is \( y = a(x - h)^2 + k \), where \((h, k)\) is the vertex of the parabola.

Step2: Determine the vertex from the graph

Looking at the graph, the vertex of the parabola is at \((6, -4)\). This means \( h = 6 \) and \( k = -4 \).

Step3: Determine the direction and stretch factor

The parabola opens downward, so \( a \) should be negative. Among the given options, the coefficient \( a = -5 \) (negative, indicating downward opening) and the vertex \((h, k)=(6, -4)\) matches the equation \( y = -5(x - 6)^2 - 4 \).

Answer:

\( y = -5(x - 6)^2 - 4 \)