Answer
See below
![](https://gradesaver.s3.amazonaws.com/uploads/solution/d31f65e7-8da9-405f-8820-a294361e4eee/result_image/1623499513.png?X-Amz-Algorithm=AWS4-HMAC-SHA256&X-Amz-Credential=AKIAJVAXHCSURVZEX5QQ%2F20240908%2Fus-east-1%2Fs3%2Faws4_request&X-Amz-Date=20240908T000822Z&X-Amz-Expires=900&X-Amz-SignedHeaders=host&X-Amz-Signature=757c5086ee8d00eca5bf40cb6f98f3da4630ceef0808e0055bbb81a9b9c9c8f9)
Work Step by Step
The intercept form of a quadratic function is:
$$y=a(x-p)(x-q)$$
where $a=1\\p=2\\q=9$
The x-intercepts occur at: $(2,0);(9,0)$
The x-coordinate of the vertex is: $x=\frac{p+q}{2}=\frac{2+9}{2}=\frac{11}{2}=5.5$
Find the y-coordinate: $y=(5.5-2)(5.5-9)=3.5(-3.5)=-12.25$
Hence, the vertex is $(5.5,-12.25)$
The axis of symmetry is $x=5.5$