Question

The graph of y = 2x2 is transformed into y = -2x2 + 3. Which of the following situations best represents the effect of transformation on the graph of the quadratic function? (Select all that apply).
he transformation vertically stretches the graph by a factor of -2.
The transformation reflects the graph over the x-axis.
The transformation shifts the graph 3 units up.
The transformation shrinks the graph by a factor of -2.
The transformation shifts the graph 2 units down.

Answer 1

Given the graph of y = 2x² is transformed into y = -2x² + 3.  

For any function y = f(x), the transformation y' = -y = -f(x) reflects the graph across x-axis.

So it means that y = -2x² is the reflection of y = 2x² across the x-axis.

For any graph y = g(x), the transformation y' = y + k = g(x) + k shifts the graph 'k' units upward for all value of 'k' > 0.

So it means that y = -2x² + 3 is the shifted version of y = -2x² by '"3 units up".

Hence, option B and C are correct i.e. "reflection across x-axis" and "shift of 3 units up".

Answer 2

I think the correct answer is B and C