Answer:
[tex]y=-(x-1)^2+2[/tex]
Step-by-step explanation:
A quadratic function in vertex form is represented as:
[tex]\begin{gathered} y=a(x-h)^2+k \\ \text{where,} \\ (h,k)\text{ is the vertex} \end{gathered}[/tex]
Given the vertex (1,2) substitute it into the function:
[tex]y=a(x-1)^2+2[/tex]
As you can see, we still do not know the value for ''a'', use the point given (4,-7) substitute it (x,y) and solve for ''a'':
[tex]\begin{gathered} -7=a(4-1)^2+2 \\ -7=a(3)^2+2 \\ -7=9a+2 \\ 9a=-7-2 \\ a=-\frac{9}{9} \\ a=-1 \end{gathered}[/tex]
Hence, the equation of the function would be:
[tex]y=-(x-1)^2+2[/tex]
