Given: A function f(x) and g(x)-
[tex]\begin{gathered} f(x)=x^2 \\ g(x)=-(x-1)^2+4 \end{gathered}[/tex]Required: To describe how the graph of both functions is related.
Explanation: The quadratic function of the form
[tex]y=ax^2+bx+c[/tex]has a y-intercept at c. Now
[tex]\begin{gathered} g(x)=-x^2-1+2x+4 \\ g(x)=-x^2+2x+3 \end{gathered}[/tex]Hence y-intercept is 3. Now in f(x) c=0. Both graphs can be related as follows
[tex]g(x)=-f(x)+2x+3[/tex]Graphical Representation is as follows-
The blue graph represents f(x) while the red graph represents g(x).
Final Answer: Given graphs are related as follows-
[tex]g(x)=-f(x)+2x+3[/tex]
