mitchell knows that $f(x) = x^2$ is the parent graph of a quadratic. what steps should he take if he wants…

mitchell knows that $f(x) = x^2$ is the parent graph of a quadratic. what steps should he take if he wants to transform the parent graph to obtain the graph of $f(x) = (x + 6)^2 - 3$?\na. he should shift it 6 units to the right and 3 units up.\nb. he should shift it 6 units to the left and 3 units up.\nc. he should shift it 6 units to the left and 3 units down.\nd. he should shift it 6 units to the right and 3 units down.

mitchell knows that $f(x) = x^2$ is the parent graph of a quadratic. what steps should he take if he wants to transform the parent graph to obtain the graph of $f(x) = (x + 6)^2 - 3$?\na. he should shift it 6 units to the right and 3 units up.\nb. he should shift it 6 units to the left and 3 units up.\nc. he should shift it 6 units to the left and 3 units down.\nd. he should shift it 6 units to the right and 3 units down.

Answer

Answer:

C. He should shift it 6 units to the left and 3 units down.

Brief Explanations:

For a quadratic function ( y = a(x - h)^2 + k ), the horizontal shift is determined by ( h ) (right if ( h>0 ), left if ( h<0 )) and vertical shift by ( k ) (up if ( k>0 ), down if ( k<0 )). The parent function is ( f(x)=x^2 ) (where ( h = 0,k = 0 )), and the transformed function is ( f(x)=(x + 6)^2-3=(x-(-6))^2+(-3) ). Here, ( h=-6 ) (so shift 6 units left) and ( k = - 3 ) (so shift 3 units down).