which function could be represented by the graph on the coordinate plane?\n○ (f(x)=(x - 8)^2+6)\n○ (f(x)=(x…

Explanation:

Step1: Identify the vertex form of a parabola.

The vertex form of a parabola is $f(x) = a(x-h)^2 + k$, where $(h, k)$ is the vertex. All options are in this form with $a=1$.

Step2: Determine the location of the vertex from the graph.

The graph shows a parabola opening upwards with its vertex located in the fourth quadrant, meaning the x-coordinate ($h$) is positive and the y-coordinate ($k$) is negative.

Step3: Analyze the vertex for each option.

Option 1: $f(x) = (x - 8)^2 + 6$. Vertex $(h, k) = (8, 6)$. Quadrant I. Option 2: $f(x) = (x + 8)^2 + 6$. Vertex $(h, k) = (-8, 6)$. Quadrant II. Option 3: $f(x) = (x + 8)^2 - 6$. Vertex $(h, k) = (-8, -6)$. Quadrant III. Option 4: $f(x) = (x - 8)^2 - 6$. Vertex $(h, k) = (8, -6)$. Quadrant IV.

Step4: Select the option matching the graph's vertex location.

The vertex from the graph is in the fourth quadrant (positive $h$, negative $k$). Option 4 has a vertex at $(8, -6)$, which is in the fourth quadrant.

Answer:

$f(x) = (x - 8)^2 - 6$