Chapter EP, Problem 5.1.6EP

(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 5.1.6EP

The value of the y intercept is 0 and equation of the symmetry is $1$ then the x coordinate of the vertex is 1.

Explanation of Solution

Given:

The given equation is $f\left(x\right)=-3x^2+6x$ .

Calculation:

Consider the given equation is,

  $f\left(x\right)=-3x^2+6x$

Then, find the y intercept as,

  $\begin{array}{c}f\left(0\right)=-3{\left(0\right)}^2+6\left(0\right)\\ =0\end{array}$

The axis of the symmetry is obtained as,

  $\begin{array}{c}x=-\frac{b}{2a}\\ =\frac{-6}{2\left(-3\right)}\\ =1\end{array}$

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 5.1.6EP

The required table is shown in Table 1.

Explanation of Solution

The given equation is $f\left(x\right)=-3x^2+6x$ .

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

Table 1

$x$	$-3x^2+6x$	$f\left(x\right)$	$\left(x,f\left(x\right)\right)$
$-1$	$-3{\left(-1\right)}^2+6\left(-1\right)$	$-9$	$\left(-1,-9\right)$
$0$	$-3{\left(0\right)}^2+6\left(0\right)$	$0$	$\left(0,0\right)$
$1$	$-3{\left(1\right)}^2+6\left(1\right)$	$3$	$\left(1,3\right)$
$2$	$-3{\left(3\right)}^2+6\left(3\right)$	$0$	$\left(2,0\right)$
$3$	$-3{\left(2\right)}^2+6\left(2\right)$	$-9$	$\left(3,-9\right)$

(c)

To determine

To Find: The graph for the function.

Answer to Problem 5.1.6EP

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