Question

1. parent:

function:
graph of a parabola opening to the left with vertex at the origin on a coordinate grid

Explanation:

Step1: Identify parent function

The graph is a horizontal parabola, parent is $x=y^2$.

Step2: Find horizontal shift

Vertex at (0,0), shifts left 2 units: $x = y^2 - 2$.

Step3: Verify with graph points

Test $y=0$: $x=0^2-2=-2$, matches. Test $y=2$: $x=2^2-2=2$, matches graph.

Answer:

1. Parent: $x=y^2$

Function: $x = y^2 - 2$