Chapter 3.1, Problem 92E

(a)

To determine

To calculate: The solution of equation $f\left(x\right)=-x^2+2x+1$ for $f\left(x\right)=0$.

(b)

To determine

To calculate: The solution of equation $f\left(x\right)=-x^2+2x+1$ for $f\left(x\right)=-10$.

(c)

To determine

To calculate: The solution of equation $f\left(x\right)=-x^2+2x+1$ for $f\left(x\right)>0$.

(d)

To determine

To calculate: The solution of equation, $f\left(x\right)=-x^2+2x+1$ for $f\left(x\right)\le 0$.

(e)

To determine

To calculate: The function $f$ in the form $f\left(x\right)=a{\left(x-h\right)}^2+k$ and describe graph of the function as a transformation of the graph of $y=x^2$.

(f)

To determine

To graph: The graph of the function and calculate the domain, range, and the maximum or minimum y-coordinate on the graph.

(g)

To determine

The relationship between the graph of function $f\left(x\right)=-x^2+2x+1$ and answers to parts (c) and (d).

(h)

To determine

To calculate: The intercepts, axis of symmetry, vertex, opening, and intervals on which function $f\left(x\right)=-x^2+2x+1$ is increasing or decreasing.