Chapter 4, Problem 12SGR

(a)

To determine

To find: The $y$ -intercept, the equation of the axis of symmetry, and the $x$ -coordinate of the vertex.

Answer to Problem 12SGR

The axis of symmetry for the equation is $x=2$ .

Explanation of Solution

Given information:

The given function is $f\left(x\right)=-3x^2+12x-1$ .

Calculation:

The function is form of $f\left(x\right)=a{x}^2+bx+c$ ,

Thus,

  $\begin{array}{l}a=-3\\ b=12\\ c=-1\end{array}$

The $y$ -intercept $c$ is $-1$ .

The $x$ -coordinate for the vertex,

  $x=\frac{-b}{2a}$ .

Substitute the value of $a,b$ in the above expression,

  $\begin{array}{c}x=\frac{-\left(12\right)}{2\left(-3\right)}\\ =2\end{array}$

Therefore, the axis of symmetry for the equation is $x=2$ .

(b)

To determine

To find: The table of value that includes the vertex.

Answer to Problem 12SGR

The solution is in table.

Explanation of Solution

Given information:

The given function is $f\left(x\right)=-3x^2+12x-1$ .

Calculation:

Consider the table for different points on the parabola.

Table $\left(1\right)$

$x$	$-3x^2+12x-1$	$f\left(x\right)$	$\left(x,f\left(x\right)\right)$
$0$	$-3{\left(0\right)}^2+12\left(0\right)-1$	$-1$	$\left(0,-1\right)$
$2$	${\left(2\right)}^2+12\left(2\right)-1$	$11$	$\left(2,11\right)$
$1$	$-3{\left(1\right)}^2+12\left(1\right)-1$	$18$	$\left(1,18\right)$

Interpretation: The given data is written in table $\left(1\right)$

(c)

To determine

To graph: The function $f\left(x\right)=-3x^2+12x-1$ .

Explanation of Solution

Given information:

The given function is $f\left(x\right)=-3x^2+12x-1$ .

Graph:

Consider the function $f\left(x\right)=-3x^2+12x-1$ .

  

Figure $\left(1\right)$

Interpretation: Graph for the $f\left(x\right)=-3x^2+12x-1$ shows in figure $\left(1\right)$ .

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