Which of the following is the maximum value of the function y=-2x^2+5

Remember that x² has minimum value 0. Multiple x² by -1 would flip it across x-axis so -x² would have maximum value 0.

Now multiplying -x² by 2 stretch it vertically, however 2 times 0 is still 0 so maximum value is still 0.

Now we add it by 5 which makes it shifts 5 units up, so this affects maximum value.

So everything will be shifted 5 units up, so new maximum would be 5.

Final 5

Hope this helps.