Final answer:
A parabola with a negative leading coefficient and an even exponent will have a maximum and its end behavior will open downwards.
Step-by-step explanation:
A parabola with a negative leading coefficient and an even exponent will have a maximum. This is because the negative leading coefficient reflects the parabola downwards, and the even exponent ensures that both ends of the parabola are symmetrical.
The end behavior of this parabola depends on whether the exponent is 2 or greater than 2. For a parabola with an even exponent greater than 2, the end behavior will be the same as a positive leading coefficient parabola, where the ends of the parabola open upwards. However, if the exponent is exactly 2 (as specified in the question), the end behavior will be the same as a negative leading coefficient parabola, where the ends of the parabola open downwards.
In summary, a parabola with a negative leading coefficient and an even exponent will have a maximum and its end behavior will open downwards.