2. The graph of \( h(x) \) is the graph of \( g(x)=(x-2)^{2}+6 \) translated 5 unis lett and 3 units down. 2. 2 pta) Whze the function \( h(x) \) in vertex form. b. (4 pos) Over what interval is \( h(x) \) incre asing? When is it decreasing? c 2 pts) How does the graph of \( h(x) \) compare to the graph of \( f(x)=x^{2} \) ?

To find the function \( h(x) \) in vertex form, we start with \( g(x) = (x-2)^2 + 6 \). Translating the graph 5 units left changes the \( x \)-coordinate of the vertex from \( 2 \) to \( -3 \) (subtracting 5), and the 3 units down reduces the \( y \)-coordinate from \( 6 \) to \( 3 \). Thus, the vertex becomes \((-3, 3)\), and the function in vertex form is: \[ h(x) = (x + 3)^2 + 3. \] The function \( h(x) \) increases when \( x \) is greater than \(-3\) and decreases when \( x \) is less than \(-3\). Specifically, \( h(x) \) is decreasing on the interval \((-∞, -3)\) and increasing on the interval \((-3, ∞)\). To visualize this, think of the vertex as the peak of a rollercoaster, where riders ascend to the top and then start their thrilling descent!