Answer
See below
![](https://gradesaver.s3.amazonaws.com/uploads/solution/1317d627-f8eb-4dde-8d3c-99f7293a2b07/result_image/1622314520.png?X-Amz-Algorithm=AWS4-HMAC-SHA256&X-Amz-Credential=AKIAJVAXHCSURVZEX5QQ%2F20240908%2Fus-east-1%2Fs3%2Faws4_request&X-Amz-Date=20240908T001349Z&X-Amz-Expires=900&X-Amz-SignedHeaders=host&X-Amz-Signature=15647cdf359af8ad596a2797340e60b72cb4aa85c2841453ad4d48f53a508aef)
Work Step by Step
The form of the quadratic function is: $y=a(x-p)(x-q)$
where $a=3\\p=-1\\q=-2$
Thus, the intercepts occur at $(-1,0)$ and $(-2,0)$
The x-coordinate of the vertex is: $x=\frac{p+q}{2}=\frac{-1+(-2)}{2}=\frac{-3}{2}=-1.5$
Find the y-coordinate: $y=3(-1.5+1)(-1.5+2)=3(-0.5)(0.5)=-0.75$
Hence, the vertex is $(-1.5,-0.75)$