Question

Question was provided via image upload.

Explanation:

Identify the vertex from the graph

Using the Vertex Form knowledge point

$$ (h, k) = (-3, -9) $$

Write the vertex form equation

Using the Vertex Form and Quadratic Transformations knowledge points

$$ g(x) = a(x - h)^2 + k \implies g(x) = a(x + 3)^2 - 9 $$

Determine the leading coefficient

Using the Quadratic Transformations knowledge point

$$
LATEXBLOCK0
$$

State the final function rule

Using the Vertex Form knowledge point

$$ g(x) = \frac{2}{3}(x + 3)^2 - 9 $$

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>\(\frac{2}{3}(x + 3)^2 - 9\)</blank>