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^2 + k ) is
solid.

use the slider to change the value of ( k )
positive values of ( k ) shift the graph
negative values of ( k ) shift the graph

down
left
right
up

( y = x^2 + k ) ( k = 0 )

Explanation:

For the quadratic function transformation \(g(x) = x^2 + k\), adding a constant \(k\) affects the vertical position of the parent function \(f(x)=x^2\). Positive \(k\) adds to the output (y-value) of each point, shifting the graph upward. Negative \(k\) subtracts from the y-value, shifting the graph downward.

Answer:

Positive values of \(k\) shift the graph: up
Negative values of \(k\) shift the graph: down