Algebra-2

To determine how the black line y = x² transforms into the red line, we can analyze the changes:

Reflection: The negative sign in front of the squared term indicates that the graph is reflected over the x-axis, changing the parabola from opening upwards to downwards.

Horizontal Shift: The term (x − 3) indicates a shift 3 units to the right.

Vertical Shift: The term −2 suggests a shift downward by 2 units.

Thus, the equation of the transformed red line is: 

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