Question

the graph shows \\(g(x)\\), which is a translation of \\(f(x) = x^2\\). write the function rule for \\(g(x)\\).

write your answer in the form \\(a(x - h)^2 + k\\), where \\(a\\), \\(h\\), and \\(k\\) are integers or simplified fractions.

\\(g(x) = \\)

Explanation:

Identify the vertex of the parabola

Using the Vertex Form knowledge point

$$ (h, k) = (0, -8) $$

Determine the vertical stretch factor

Using the Quadratic Transformations knowledge point

$$
LATEXBLOCK0
$$

Write the final function rule

Using the Vertex Form knowledge point

$$ g(x) = (x - 0)^2 - 8 $$

Answer:

The graph shows \(g(x)\), which is a translation of \(f(x) = x^2\). Write the function rule for \(g(x)\).

Write your answer in the form \(a(x - h)^2 + k\), where \(a\), \(h\), and \(k\) are integers or simplified fractions.

\(g(x) =\) <blank>\((x - 0)^2 - 8\)</blank>