Answer:
An equation of the new function in vertex form is [tex]y=\left ( x-7 \right )^2+2[/tex].
Step-by-step explanation:
Consider parent function as [tex]y=x^{2}[/tex].
According to the transformation of graph,
The function [tex]f\left ( x-b \right )[/tex] shifts the function to right side by b units.
So in this case, graph is translated to the right side by 7 units, so the parent function [tex]y=x^{2}[/tex] can be written as [tex] y=\left ( x-7 \right )^2 [/tex]
The function [tex]f\left ( x \right )+b[/tex] shifts the function in upward direction by b units.
So in this case, graph is translated in upward by 2 units, so the function [tex] y=\left ( x-7 \right )^2 [/tex] can be written as [tex] y=\left ( x-7 \right )^2+2 [/tex]
Now vertex form of quadratic equation is given as, [tex]y=a\left ( x-h \right )^2+k[/tex]
So the final equation is [tex]y=\left ( x-7 \right )^2+2[/tex]. .
