Question

find the vertex and axis of symmetry of $f(x)=3(x + 5)^2+1$. the vertex is ( , ). the axis of symmetry is $x=$

Explanation:

Step1: Recall vertex - form of a quadratic function

The vertex - form of a quadratic function is $y = a(x - h)^2+k$, where the vertex is $(h,k)$ and the axis of symmetry is $x = h$.
For the function $f(x)=3(x + 5)^2+1$, we can rewrite it as $f(x)=3(x-(- 5))^2 + 1$.

Step2: Identify the vertex

Comparing $f(x)=3(x-(-5))^2 + 1$ with $y=a(x - h)^2+k$, we have $h=-5$ and $k = 1$. So the vertex is $(-5,1)$.

Step3: Identify the axis of symmetry

Since the axis of symmetry is $x = h$ and $h=-5$, the axis of symmetry is $x=-5$.

Answer:

The vertex is $(-5,1)$. The axis of symmetry is $x=-5$.