Chapter 9.1, Problem 67PPS

(a)

To determine

The related function of the equation.

Answer to Problem 67PPS

The value of y is kept on one side and the remaining terms are moved aside.

Explanation of Solution

Given information:

The functions are $x^2-x=12$ ; $x^2+8x=9$ ; $x^2=14x-24$ ; $x^2+16x=-28$

Formula used:

Related functions are given in terrns of y.

Calculation:

Equation	Related Function
$x^2-x=12$	$y=x^2-x-12$
$x^2+8x=9$	$y=x^2+8x-9$
$x^2=14x-24$	$y=x^2-14x+24$
$x^2+16x=-28$	$y=x^2+16x+28$

Conclusion:

The value of y is kept on one side.

(b)

To determine

The graph of the function.

Explanation of Solution

Given information:

Graph each related function with calculator.

Formula used:

The graph is drawn between x and y axis.

Calculation:

Let $Y1=x^2–x–12$ . Select 6 Under the ZOOM adjust the viewing window to standard.

Let $Y1=x^2\text{+ }8x-9$ . Use the WINDOW option to viewing window.

  

Let $Y1=x^2-14x+24$ . Use the WINDOW option viewing window. 

  

Let $Y1=x^2+16x+28$ . Use the WINDOW option viewing window. 

  

Conclusion:

The graph is plotted using graphical calculator.

(c)

To determine

The number of zeros that is being related to the function.

Answer to Problem 67PPS

The y values are obtained for all the functions.

Explanation of Solution

Given information:

Use the table feature on your c determines the zeros of each related function. Record the table above. Also record the values of the function than and one unit more than each zero.

Formula used:

Putting zero for the function to determine the y value.

Calculation:

Let $Y1=x^2–x–12$ . Use the 2nd [TABLE] option table of values. Use the up and down arrow to locate where Y1 = 0. Identify the y -values above and below

X	Y1		X	Y1
-4	8		-1	-10
-3	0		0	-12
-2	-6		1	-12
-1	-10		2	-10
0	-12		3	-6
1	-12		4	0
2	-10		5	8
X=-4			X=4

Let $Y1=x^2+8x-9$ . Use the 2nd [TABLE] option table of values. Use the up and down arrow to locate where Y1 = 0. Identify the y -values above and below

X	Y1		X	Y1
-10	11		-4	-25
-9	0		-3	-24
-8	-9		-2	-21
-7	-16		-1	-16
-6	-21		0	-9
-5	-24		1	0
-4	-25		2	11
X=-10			X=2

Let Y1 = x 2 - 14x + 24. Use the 2nd [TABLE] option a table of values. Use the up and down arrow to loc where Y1 = 0. Identify the y -values above and below,

X	Y1		X	Y1
1	11		7	-25
2	0		8	-24
3	-9		9	-21
4	-16		10	-16
5	-21		11	-9
6	-24		12	0
7	-25		13	11
X=1			X=12

Let $Y1=x^2+16x+28$ . Use the 2nd [TABLE] option a table of values. Use the up and down arrow to loc where Y1 = 0. Identify the y -values above and below,

X	Y1		X	Y1
-15	13		-7	-35
-14	0		-6	-32
-13	-11		-5	-27
-12	-20		-4	-20
-11	-27		-3	-11
-10	-32		-2	0
9	-35		-1	13
X=14			X=-2

Conclusion:

The y values are obtained for all the functions.

(d)

To determine

The function values for x values.

Answer to Problem 67PPS

It contains the opposite sign before zero.

Explanation of Solution

Given information:

The function values for x-value and just after a zero.

Formula used:

Substituting x value to zero.

Calculation:

The function values have opposite signs before a zero

Conclusion:

It contains the opposite sign before zero.