Chapter 8.8, Problem 10WE

To determine

To find: Thecoordinates of the vertex, the equation of the axis of symmetry and the least value of the function.

Answer to Problem 10WE

The coordinate of the vertex is $\left(1,-1\right)$ , the equation of the symmetry is $x=1$ , and the least value of the function is $-1$ .

Explanation of Solution

Given information:

The given equation is,

  $t\left(x\right)=4-10x+5x^2$

The x -coordinate of the vertex is calculated as,

  $\begin{array}{c}x=-\frac{b\left(\text{coefficent of }x\right)}{2a\left(\text{coefficent of }{x}^2\right)}\\ =-\frac{\left(-10\right)}{2\left(5\right)}\\ =1\end{array}$

The y -coordinate of the vertex is calculated as,

  $\begin{array}{l}t\left(x\right)=4-10x+5x^2\\ t\left(1\right)=4-10\left(1\right)+5{\left(1\right)}^2\\ y=-1\end{array}$

The coordinate of the vertex is $\left(1,-1\right)$ .

The equation of axis od symmetry is calculated as,

  $\begin{array}{c}x=-\frac{b\left(\text{coefficent of }x\right)}{2a\left(\text{coefficent of }{x}^2\right)}\\ =-\frac{\left(-10\right)}{2\left(5\right)}\\ x=1\end{array}$

Thus, the coordinate of the vertex is $\left(1,-1\right)$ , the equation of the symmetry is $x=1$ , and the least value of the function is $-1$ .