Question

exploring translations of the quadratic parent function
the graph of the parent function ( f(x) = x^2 ) is dashed and
the graph of the transformed function ( g(x) = (x - h)^2 ) is
solid

use the slider to change the value of ( h ). how does
changing the value of ( h ) affect the vertex?
if ( h = 3 ), the vertex shifts to
if ( h = -5 ), the vertex shifts to
( (-3, 0) )
( (0, -3) )
( (0, 3) )
( (3, 0) )

( y = (x - h)^2 )
( h = 0 )

Explanation:

Step1: Recall vertex of parent function

The parent function $f(x)=x^2$ has vertex at $(0,0)$.

Step2: Apply horizontal shift rule

For $g(x)=(x-h)^2$, the vertex shifts to $(h,0)$.

Step3: Calculate vertex for $h=3$

Substitute $h=3$: $(3, 0)$

Step4: Calculate vertex for $h=-5$

Substitute $h=-5$: $(-5, 0)$

Answer:

If $h=3$, the vertex shifts to (3, 0)
If $h=-5$, the vertex shifts to (-5, 0)