y=-x squared+3x

Question

use a table of values to graph each function.

Answer 1

For this problem you need to remember the rules for adding/multiplying negative and positive numbers.  A negative times a negative is positive.  A positive times a positive is positive.  A negative times a positive is negative.  Adding opposite signs, subtract the numbers and take the sign of the bigger number.  Adding numbers with same signs, add the numbers and keep the same sign.  You also need to know that x² = x times x
x                -x² + 3x                                                     y

-2             -(-2)² + 3(-2)  = -4 +- 6 = -10                   -10

-1            - (-1)² + 3(-1) = -1 + -3 = -4                       -4

0             - (0)² + 3(0) = 0 +0 =0                                0

1             -(1)² + 3(1)  = -1 + 3 = 2                            2

Also note the if the original equation was (-x)² + 3X  the answers would be as follows:

x          (-x)² + 3x                                   y

-2         (-(-2))² + 3(-2) = 4 + -6=-2         -2

-1         (-(-1))² + 3(-1) = 1 + -3= -2        -2

0          (-0)² + 3(0)  = 0                          0

1          (-1)² + 3(1) = 1+3=4                   4

2          (-2)² + 3(2) = 4+6=10                10

Answer 2

A table of values can be created by choosing a value for X, plugging in that value in the equation, and then using the result as the Y value as seen below (I'm sorry I don't have a better way to represent the table):

X  -4   -3  -2  -1 0  1  2  3   4   5    6    7
Y -28 -18 -10 -4 0  2  2  0  -4 -10 -18 -28

In the creation of this table, be very careful to use the proper order of operations. If the first part of the equation is: -x² and not (-x)², then only the x value is squared and then is negated.

Finally, plot these points and draw the curve.

Answer 3