Question

find the equation of the axis of symmetry of the following quadratic equation.
$f(x) = 5(x + 2)^2 + 1$

Explanation:

Step1: Recall vertex form of parabola

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

Step2: Identify \( h \) from given function

Given \( f(x)=5(x + 2)^2+1 \), rewrite \( (x + 2) \) as \( (x - (-2)) \). So comparing with \( a(x - h)^2 + k \), we have \( h=-2 \).

Step3: Determine axis of symmetry

Since the axis of symmetry is \( x = h \), substituting \( h = -2 \), the equation of the axis of symmetry is \( x=-2 \).

Answer:

\( x = -2 \)