document.write( "Question 156294: Evaluate the functions for the values of x given as 1, 2, 4, 8, and 16. Describe the differences in the rate at which each function changes with increasing values of x. \r
\n" ); document.write( "\n" ); document.write( "2. f(x) = x2 - 3x + 2 \r
\n" ); document.write( "\n" ); document.write( " \n" ); document.write( "

Algebra.Com's Answer #115096 by jim_thompson5910(35256) $\"\"$ $\"About$

You can put this solution on YOUR website!
# 2\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "Let's find the function value when $\"x=1\"$ :\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( " $\"y=x%5E2-3x%2B2\"$ Start with the given equation.\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( " $\"y=%281%29%5E2-3%281%29%2B2\"$ Plug in $\"x=1\"$ .\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( " $\"y=1%281%29-3%281%29%2B2\"$ Square $\"1\"$ to get $\"1\"$ .\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( " $\"y=1-3%281%29%2B2\"$ Multiply $\"1\"$ and $\"1\"$ to get $\"1\"$ .\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( " $\"y=1-3%2B2\"$ Multiply $\"-3\"$ and $\"1\"$ to get $\"-3\"$ .\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( " $\"y=0\"$ Combine like terms.\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "So if $\"x=1\"$ , then $\"y=0\"$ .\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "-------------\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "Let's find the function value when $\"x=2\"$ :\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( " $\"y=x%5E2-3x%2B2\"$ Start with the given equation.\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( " $\"y=%282%29%5E2-3%282%29%2B2\"$ Plug in $\"x=2\"$ .\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( " $\"y=1%284%29-3%282%29%2B2\"$ Square $\"2\"$ to get $\"4\"$ .\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( " $\"y=4-3%282%29%2B2\"$ Multiply $\"1\"$ and $\"4\"$ to get $\"4\"$ .\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( " $\"y=4-6%2B2\"$ Multiply $\"-3\"$ and $\"2\"$ to get $\"-6\"$ .\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( " $\"y=0\"$ Combine like terms.\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "So if $\"x=2\"$ , then $\"y=0\"$ .\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "-------------\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "Let's find the function value when $\"x=4\"$ :\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( " $\"y=x%5E2-3x%2B2\"$ Start with the given equation.\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( " $\"y=%284%29%5E2-3%284%29%2B2\"$ Plug in $\"x=4\"$ .\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( " $\"y=1%2816%29-3%284%29%2B2\"$ Square $\"4\"$ to get $\"16\"$ .\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( " $\"y=16-3%284%29%2B2\"$ Multiply $\"1\"$ and $\"16\"$ to get $\"16\"$ .\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( " $\"y=16-12%2B2\"$ Multiply $\"-3\"$ and $\"4\"$ to get $\"-12\"$ .\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( " $\"y=6\"$ Combine like terms.\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "So if $\"x=4\"$ , then $\"y=6\"$ .\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "-------------\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "Let's find the function value when $\"x=8\"$ :\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( " $\"y=x%5E2-3x%2B2\"$ Start with the given equation.\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( " $\"y=%288%29%5E2-3%288%29%2B2\"$ Plug in $\"x=8\"$ .\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( " $\"y=1%2864%29-3%288%29%2B2\"$ Square $\"8\"$ to get $\"64\"$ .\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( " $\"y=64-3%288%29%2B2\"$ Multiply $\"1\"$ and $\"64\"$ to get $\"64\"$ .\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( " $\"y=64-24%2B2\"$ Multiply $\"-3\"$ and $\"8\"$ to get $\"-24\"$ .\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( " $\"y=42\"$ Combine like terms.\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "So if $\"x=8\"$ , then $\"y=42\"$ .\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "-------------\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "Let's find the function value when $\"x=16\"$ :\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( " $\"y=x%5E2-3x%2B2\"$ Start with the given equation.\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( " $\"y=%2816%29%5E2-3%2816%29%2B2\"$ Plug in $\"x=16\"$ .\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( " $\"y=1%28256%29-3%2816%29%2B2\"$ Square $\"16\"$ to get $\"256\"$ .\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( " $\"y=256-3%2816%29%2B2\"$ Multiply $\"1\"$ and $\"256\"$ to get $\"256\"$ .\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( " $\"y=256-48%2B2\"$ Multiply $\"-3\"$ and $\"16\"$ to get $\"-48\"$ .\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( " $\"y=210\"$ Combine like terms.\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "So if $\"x=16\"$ , then $\"y=210\"$ .\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "-------------\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "Now let's make a table of the values we just found.\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "Jump to Top of Page\r
\n" ); document.write( "\n" ); document.write( "

Table of Values:

\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "x y
1 0
2 0
4 6
8 42
16 210\r\n" );
document.write( "\r\n" );
document.write( "

\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "Because the function is a quadratic, this means that the polynomial undergoes quadratic growth. This is faster than linear growth.\r
\n" ); document.write( "\n" ); document.write( " \n" ); document.write( "

\n" );