Question

if the parabola of the form $y = a(x - h)^2 + k$ is always shifted horizontally $h$ units and vertically $k$ units, then its vertex is always\
$(-h, -k)$\
$(h, k)$\
$(-h, k)$\
$(h, -k)$\
complete\
enter the coordinates of the vertex of the graph of $y = 2(x + 5)^2 - 4$.\
vertex: ( , )\
done

Explanation:

Step1: Recall Vertex Form

The vertex form of a parabola is \( y = a(x - h)^2 + k \), where \((h, k)\) is the vertex.

Step2: Rewrite Given Equation

Given \( y = 2(x + 5)^2 - 4 \), rewrite \( x + 5 \) as \( x - (-5) \). So the equation becomes \( y = 2(x - (-5))^2 + (-4) \).

Step3: Identify h and k

Comparing with \( y = a(x - h)^2 + k \), we have \( h = -5 \) and \( k = -4 \).

Answer:

\((-5, -4)\)