Which of the following describes the translation of the graph of y = x2 to obtain the graph of y = -x2 + 3?

reflect over the x-axis and shift right 3

reflect over the x-axis and shift up 3

reflect over the y-axis and shift down 3

Reflect over the x-axis and shift up 3.

Step-by-step explanation:

Given  : translation of the graph of y = x² to obtain the graph of y = -x² + 3.

To find  : Which of the following describes the translation of the graph.

Solution : We have given that

Parent function  y = x²

Translated function  y = -x² + 3.

By the translation rule : f(x) →→→→→→ -f(x) it mean function reflected over x axis.

f(x) →→→→→→ f(x)+h it mean function shifted up by h unit.

Since , graph of  y = -x²+3 reflected over x axis and shifted up by 3 unit with

y = x².

Therefore, Reflect over the x-axis and shift up 3.