Chapter 4, Problem 10SGR

(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 10SGR

The axis of symmetry for the equation is $x=3.5$ .

Explanation of Solution

Given information:

The given function is $f\left(x\right)=x^2-7x+15$ .

Calculation:

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

Thus,

  $\begin{array}{l}a=1\\ b=-7\\ c=15\end{array}$

The $y$ -intercept $c$ is $15$ .

The $x$ -coordinate for the vertex,

  $x=\frac{-b}{2a}$ .

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

  $\begin{array}{c}x=\frac{-\left(-7\right)}{2\left(1\right)}\\ =3.5\end{array}$

Therefore, the axis of symmetry for the equation is $x=3.5$ .

(b)

To determine

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

Answer to Problem 10SGR

The table is shown below.

Explanation of Solution

Given information:

The given function is $f\left(x\right)=x^2-7x+15$ .

Calculation:

Consider the table for different points on the parabola.

Table $\left(1\right)$

$x$	$x^2-7x+15$	$f\left(x\right)$	$\left(x,f\left(x\right)\right)$
$0$	${\left(0\right)}^2-7\left(0\right)+15$	$15$	$\left(0,15\right)$
$3.5$	${\left(3.5\right)}^2-7\left(3.5\right)+15$	$2.75$	$\left(3.5,2.75\right)$
$1$	${\left(1\right)}^2-7\left(1\right)+15$	$9$	$\left(1,9\right)$

Table $\left(1\right)$

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

(c)

To determine

To graph: The function $f\left(x\right)=x^2-7x+15$ .

Explanation of Solution

Given information:

The given function is $f\left(x\right)=x^2-7x+15$ .

Graph:

Consider the function $f\left(x\right)=x^2-7x+15$ .

  

Figure $\left(1\right)$

Interpretation: Graph for the $f\left(x\right)=x^2-7x+15$ shows in figure $\left(1\right)$ .

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