Question 60810
How does the graph of the quadratic function or the absolute value function change if you subtract something from them?
They cause a vertical shift down that many units.
y=x^2  and y=x^2-3 are graphed below the -3 caused a vertical shift down 3 units
{{{graph(300,200,-10,10,-10,10,x^2,x^2-3)}}}
Y=|x| and y=|x|-3 are graphed below and the -3 caused the same vertical shift down three units.
{{{graph(300,200,-10,10,-10,10,abs(x),abs(x)-3)}}}
:
When the 3 is subtracted from the x  it causes a horizontal shift to the right three units.
y=x^2 and y=(x-3)^2 are graphed below.
{{{graph(300,200,-10,10,-10,10,x^2,(x-3)^2)}}}
y=|x| and y=|x-3| are graphed below.
{{{graph(300,200,-10,10,-10,10,abs(x),abs(x-3))}}}
Happy Calculating!!!