Algebra Know-It-ALL

and

y= (x− 1)^2 − 12

How will this affect the graph of the second equation, shown by the dashed curve? How will

it affect the real solution set?

Answer 28-8

If we subtract 12 from the right side of this equation, we reduce all values of the function

by 12. This moves the entire graph of the function vertically down by 12 units. Figure 30-9

shows the result. On the x axis, each increment is 1/2 unit. On the y axis, each increment

is 2 units. This graph suggests that the resulting system still has one real solution, but it has

changed. If we want to find the solution, we must solve the new system, starting all over again

from scratch. (For extra credit, you can do this.)

Question 28-9

Consider the system of equations we solved in Answer 27-9:

y= (x+ 1)^3

and

y=x^3 + 2 x^2 +x

How can we sketch an approximate graph of this system, showing the real solution?

x

y

No

real

solutions

No

intersection

points

Figure 30-8 Illustration for Answer

28-7. The first function is

graphed as a solid curve;

the second function is

graphed as a dashed curve.

The curves do not intersect,

indicating that the system

has no real solutions. On

thex axis, each increment

is 1/2 unit. On the y axis,

each increment is 2 units.

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