Chapter EP, Problem 5.1.9EP

(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 5.1.9EP

The value of the y intercept is $12$ and equation of the symmetry is $-1$ then the x coordinate of the vertex is $-1$ .

Explanation of Solution

Given:

The given equation is $f\left(x\right)=-3x^2-6x+12$ .

Calculation:

Consider the given equation is,

  $f\left(x\right)=-3x^2-6x+12$

Then, find the y intercept as,

  $\begin{array}{c}f\left(0\right)=-3{\left(0\right)}^2-6\left(0\right)+12\\ =12\end{array}$

The axis of the symmetry is obtained as,

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

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 5.1.9EP

The required table is shown in Table 1.

Explanation of Solution

The given equation is $f\left(x\right)=-3x^2-6x+12$ .

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

Table 1

$x$	$-3x^2-6x+12$	$f\left(x\right)$	$\left(x,f\left(x\right)\right)$
$-3$	$-3{\left(-3\right)}^2-6\left(-3\right)+12$	$3$	$\left(-3,3\right)$
$-2$	$-3{\left(-2\right)}^2-6\left(-2\right)+12$	$12$	$\left(-2,12\right)$
$-1$	$-3{\left(-1\right)}^2-6\left(-1\right)+12$	$15$	$\left(-1,15\right)$
$0$	$-3{\left(0\right)}^2-6\left(0\right)+12$	$12$	$\left(0,12\right)$
$1$	$-3{\left(1\right)}^2-6\left(1\right)+12$	$3$	$\left(1,3\right)$

(c)

To determine

To Find: The graph for the function.

Answer to Problem 5.1.9EP

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