Question

SMP 7 Describe how the graph ofg(x) = -(x-1)² + 4 is related to the graph off(x)=x².

Answer 1

Given: A function f(x) and g(x)-

`\begin{gathered} f(x)=x^2 \\ g(x)=-(x-1)^2+4 \end{gathered}`

Required: To describe how the graph of both functions is related.

Explanation: The quadratic function of the form

`y=ax^2+bx+c`

has a y-intercept at c. Now

`\begin{gathered} g(x)=-x^2-1+2x+4 \\ g(x)=-x^2+2x+3 \end{gathered}`

Hence y-intercept is 3. Now in f(x) c=0. Both graphs can be related as follows

`g(x)=-f(x)+2x+3`

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-

`g(x)=-f(x)+2x+3`