Question 23010
Begin with {{{f(x) = x^2}}}

{{{graph(300,300, -10, 10, -10,10, x^2 ) }}}


Next, what happens if you make that {{{ (1/2)*x^2}}}?

{{{graph(300,300, -10, 10, -10,10, (1/2)*x^2 ) }}}
Answer:  It opens the graph up to a broader shape!


Now, what happens if you make the function negative {{{-(1/2)*x^2 }}}
{{{graph(300,300, -10, 10, -10,10, -(1/2)*x^2 ) }}}
Answer:  It inverts the graph!


Now what happens if you make that {{{-(1/2)*(x-3)^2}}}

{{{graph(300,300, -10, 10, -10,10, -(1/2)*(x-3)^2 ) }}}
Answer:  It moves the graph 3 units to the right!


Finally, what happens if you subtract 3 from the previous function?
{{{graph(300,300, -10, 10, -10,10, -(1/2)*(x-3)^2 -3) }}}
Answer:  It moves the graph down three units.


Pretty neat, huh??


R^2 at SCC