Chapter 4, Problem 1PT

(a)

To determine

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

Answer to Problem 1PT

The $y-$ intercept $c$ is $-7$ , $x-$ coordinate for vertex is $\frac{-b}{2a}$ and the axis of symmetry of the function is $-2$ .

Explanation of Solution

Given information:

The given function is $f(x)=x^2+4x-7$ .

Calculation:

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

Consider the following values,

  $\begin{array}{l}a=1\\ b=4\\ c=-7\end{array}$

The y-intercept c is $-7$ .

The $x-$ coordinate for the vertex will be,

  $x=\frac{-b}{2a}$

Substitute the value in the above expression,

  $\begin{array}{c}x=\frac{-(4)}{2(1)}\\ =-2\end{array}$

The axis of symmetry for the above equation will be $-2$ .

Therefore, $y-$ intercept $c$ is $-7$ , $x-$ coordinate for vertex is $\frac{-b}{2a}$ and the axis of symmetry is $-2$ .

(b)

To determine

To draw: The table of the values of the vertex.

Answer to Problem 1PT

The following table is shown below in table (1).

Explanation of Solution

Given information:

The given function is $f(x)=x^2+4x-7$ .

Calculation:

Consider the following table for different points on the parabola.

Table(1)

$x$	$x^2+4x-7$	$f(x)$	$(x,f(x))$
$0$	${(0)}^2+4(0)-7$	$-7$	$(0,7)$
$-2$	${(-2)}^2+4(-2)-7$	$-11$	$(-2,-11)$
$1$	${(1)}^2+4(1)+-7$	$-2$	$(1,2)$

The given data is written above in the table (1).

(c)

To determine

To graph: The function $f(x)=x^2+4x-7$ .

Explanation of Solution

Given information:

The given function is $f(x)=x^2+4x-7$ .

Graph:

Consider the function $f(x)=x^2+4x-7$

The graph for the given functions $f(x)=x^2+4x-7$ is shown in figure (1).

  

Figure (1)

Interpretation: Graph for the functions $f(x)=x^2+4x-7$ shows in figure (1).