Question

identify the vertex, axis of symmetry, and direction of the graph of each function. compare the width of the graph to the width of the graph of ( f(x)=x^2 ).
( f(x) = 6(x + 5)^2 + 5 )
the vertex is
(type an ordered pair.)

Explanation:

Step1: Recall the vertex form of a quadratic function

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

Step2: Identify \(h\) and \(k\) from the given function

For the function \( f(x)=6(x + 5)^2+5 \), we can rewrite \( x + 5\) as \( x-(-5) \). So comparing with \( f(x)=a(x - h)^2 + k \), we have \( h=-5 \) and \( k = 5 \).

Answer:

\((-5,5)\)