Question

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

Explanation:

Step1: Recall vertex - form of a parabola

The vertex - form of a parabola is $y=a(x - h)^2+k$, where $(h,k)$ is the vertex of the parabola and the axis of symmetry is the line $x = h$.

Step2: Identify $h$ and $k$ values

For the function $f(x)=-(x - 5)^2+2$, we have $a=-1$, $h = 5$ and $k = 2$.

Step3: Determine the vertex

The vertex of the parabola is $(h,k)=(5,2)$.

Step4: Determine the axis of symmetry

The axis of symmetry is given by the equation $x=h$. So, the axis of symmetry is $x = 5$.

Answer:

The vertex is $(5,2)$. The axis of symmetry is $x = 5$.