Algebra Know-It-ALL

Again, we let x be the independent variable, and then we manipulated the equations to obtain
y as a function of x in both cases. That gave us

y=− 2 x^2 − 3 x− 4

and

y=− 3 x^2 − 5 x+ 11

First, we tabulate some points

Table 28-2 shows some values of x, along with the results of plugging those values into the
above functions and churning out the arithmetic. We can start building the table by entering
the two solutions, which we determined in Chap. 27. They are

(x,y)= (−5,−39)

and

(x,y)= (3, −31)

These solutions are written as bold numerals. The other values are chosen to produce
graph points in the vicinity of the solutions. We can choose a couple of x-values less than
−5, two more between −5 and 3, and two more larger than 3. Then we can calculate the
values of the functions, and write them in the middle and right-hand columns of the
table.

Two Quadratics 467

Table 28-2. Selected values for graphing the functions

y=− 2 x^2 − 3 x− 4 and y = − 3 x^2 − 5 x+ 11.

Bold entries indicate real solutions.

x − 2 x^2 − 3 x− 4 − 3 x^2 − 5 x+ 11

− 10 − 174 − 239

− 7 − 81 − 101

− 5 − 39 − 39

− 2 −6 9

0 −4 11

3 − 31 − 31

6 − 94 − 127

9 − 193 − 277