Question

use the graph of the function $f(x) = -(x + 1)^2 + 2$. identify the vertex and the axis of symmetry.
the axis of symmetry is $x =$ choose...
the vertex is ( choose..., choose... ).

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

Step2: Match given function to vertex form

For $f(x)=-(x+1)^2+2$, rewrite as $f(x)=-(x-(-1))^2+2$. Here, $h=-1$, $k=2$.

Step3: Identify axis of symmetry

Axis of symmetry is $x=h$, so $x=-1$.

Step4: Identify vertex

Vertex is $(h,k)$, so $(-1,2)$.

Answer:

The axis of symmetry is $x=-1$
The vertex is $(-1, 2)$