Question

representing a graph with a function

which function represents profit, \\(p(x)\\), as a function of \\(x\\), the price per music class?

\\(p(x) = -(x - 6)^2 + 116\\)
\\(p(x) = (x + 6)^2 + 116\\)
\\(p(x) = -2(80^x)\\)
\\(p(x) = -80(2^x)\\)

Explanation:

Identify the vertex of the parabolic data

Using the Profit Function Modeling and Quadratic Modeling Interpretation knowledge points
The plotted points show a symmetric parabolic shape opening downward. The highest point on the graph is the vertex, which is labeled as \((6, 116)\).

Write the quadratic function in vertex form

Using the Quadratic Modeling Interpretation knowledge point

$$ P(x) = a(x - h)^2 + k $$

$$ P(x) = a(x - 6)^2 + 116 $$

Determine the leading coefficient

Using the Quadratic Modeling Interpretation knowledge point

$$
LATEXBLOCK0
$$

Formulate the final equation

Using the Profit Function Modeling knowledge point

$$ P(x) = -(x - 6)^2 + 116 $$

Answer:

• P(x) = -(x - 6)^2 + 116 (Correct answer)
• P(x) = (x + 6)^2 + 116
• P(x) = -2(80^x)
• P(x) = -80(2^x)