Question

select the correct answer.

which function does this graph represent?

\\(f(x) = 3(x + 1)^2 + 2\\)

\\(f(x) = -3(x + 1)^2 + 2\\)

\\(f(x) = -3(x + 1)^2 - 2\\)

\\(f(x) = 3(x - 1)^2 + 2\\)

Explanation:

Identify the vertex of the parabola from the graph

$$ (h, k) = (-1, 2) $$

Write the vertex form of the quadratic function

$$ f(x) = a(x - h)^2 + k = a(x + 1)^2 + 2 $$

Determine the value of the leading coefficient using a known point

$$
LATEXBLOCK0
$$

Answer:

• \(f(x) = 3(x + 1)^2 + 2\)
• \(f(x) = -3(x + 1)^2 + 2\) (Correct answer)
• \(f(x) = -3(x + 1)^2 - 2\)
• \(f(x) = 3(x - 1)^2 + 2\)