Chapter EP, Problem 5.1.8EP

(a)

To determine

To Find: The y intercept of the equation of the axis of symmetry and the x coordinate of the vertex.

Answer to Problem 5.1.8EP

The value of the y intercept is $-8$ and equation of the symmetry is $1$ then the x coordinate of the vertex is $1$ .

Explanation of Solution

Given:

The given equation is $f\left(x\right)=x^2-2x-8$ .

Calculation:

Consider the given equation is,

  $f\left(x\right)=x^2-2x-8$

Then, find the y intercept as,

  $\begin{array}{c}f\left(0\right)={\left(0\right)}^2-2\left(0\right)-8\\ =-8\end{array}$

The axis of the symmetry is obtained as,

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

The equation of the symmetry is $1$ then the x coordinate of the vertex is $1$ .

(b)

To determine

To Find: The table of the values that includes the vertex.

Answer to Problem 5.1.8EP

The required table is shown in Table 1.

Explanation of Solution

The given equation is $f\left(x\right)=x^2-2x-8$ .

The Table for the values that includes the vertex is shown in Table 1.

Table 1

$x$	$x^2-2x-8$	$f\left(x\right)$	$\left(x,f\left(x\right)\right)$
$-1$	${\left(-1\right)}^2-2\left(-1\right)-8$	$-5$	$\left(-1,-5\right)$
$0$	${\left(-1\right)}^2-2\left(-1\right)-8$	$-8$	$\left(0,-8\right)$
$1$	${\left(-1\right)}^2-2\left(-1\right)-8$	$-9$	$\left(1,-9\right)$
$2$	${\left(-1\right)}^2-2\left(-1\right)-8$	$-8$	$\left(2,-8\right)$
$3$	${\left(-1\right)}^2-2\left(-1\right)-8$	$-5$	$\left(3,-5\right)$

(c)

To determine

To Find: The graph for the function.

Answer to Problem 5.1.8EP

The required graph is shown in Figure 1.

Explanation of Solution

From the values of table 1 the graph is shown in Figure 1.

  

Figure 1