Question 1170359

The standard form of a quadratic function presents the function in the form

{{{f(x)=a(x-h)^2+k}}}

where ({{{h}}},{{{ k}}}) is the vertex.

If {{{k>0}}}, the graph shifts upward, whereas if {{{k<0}}}, the graph shifts downward.

The standard form is useful for determining how the graph is transformed from the graph of {{{y=x^2}}}. The figure below is the graph of this basic function.

{{{ graph( 600, 600, -10, 10, -10, 10, x^2) }}}


You can represent a horizontal (left, right) shift of the graph of {{{f(x)=x^2}}} by adding or subtracting a constant,{{{ h}}}, to the variable {{{x}}}, before squaring.

{{{f(x)=(x-h)^2}}}

If {{{h>0}}}, the graph shifts toward the right and if{{{ h<0}}}, the graph shifts to the left.


if given the function whose graph is the graph of {{{y=x^2}}}, but is shifted to the right {{{5}}} units, means {{{h=5}}} and function will be

{{{y=(x-5)^2}}}


{{{ graph( 600, 600, -10, 10, -10, 10, x^2, (x-5)^2) }}}