Answer
See explanation
Work Step by Step
Finding the quadratic function in standard form $f(x)=a(x-h)^2+k$:
$$f(x)=-x^2+2x+5$$ $$f(x)=-(x^2-2x)+5$$ $$f(x)=-\left(x^2-2x+\left(\frac{-2}{2}\right)^2\right)+5+\left(\frac{-2}{2}\right)^2$$ $$f(x)=-(x^2-2x+1)^2+5+1$$ $$f(x)=-\left(x-1\right)^2+6$$
The sketch of the graph of the function is as shown.
Notice that the vertex is: $$\left(1,6\right)$$
The axis of symmetry is: $$x=1$$
The $x$-intercepts are: $$(-1.45,0),(3.45,0)$$
