Chapter 8, Problem 39CT

To determine

To find: The coordinates of the vertex and the equation of the axis of symmetry of the graph of the given equation.

Answer to Problem 39CT

The coordinates of the vertex is $\left(1,1\right)$ and the equation of axis of symmetry is $x=1$ .

Explanation of Solution

Given information:

The given equation is $y=2x-x^2$ .

Calculation:

The given equation is.

  $\begin{array}{l}y=2x-x^2\\ y=-x^2+2x\end{array}$

Calculate the $x$ coordinate of the vertex.

  $\begin{array}{l}-\frac{b}{2a}\\ =\frac{-2}{2\left(-1\right)}\\ =1\end{array}$

Calculate the $y$ coordinate of the vertex.

  $\begin{array}{c}y=-x^2+2x\\ =-1+2\\ =1\end{array}$

Calculate the equation of axis of symmetry.

  $\begin{array}{c}x=-\frac{2}{2\left(-1\right)}\\ =1\end{array}$

The coordinate through which the graph passes are shown in below table.

  

The graph is shown in figure (1).

  

Figure (1)

Therefore, the coordinates of the vertex is $\left(1,1\right)$ and the equation of axis of symmetry is $x=1$ .