Question

question 19 of 23
1 point
how do you know if the parabola has a maximum or minimum?
select the correct response:

if the b is a positive, it has a maximum.
if the b is a negative, it has a minimum.

if the b is a positive, it has a minimum.
if the b is a negative, it has a maximum.

if the a is a positive, it has a maximum.
if the a is a negative, it has a minimum.

if the a is a positive, it has a minimum.
if the a is a negative, it has a maximum.

Explanation:

To determine if a parabola (in the form \( y = ax^2 + bx + c \)) has a maximum or minimum, we look at the coefficient \( a \). If \( a>0 \), the parabola opens upward, so it has a minimum point (the vertex is the lowest point). If \( a < 0 \), the parabola opens downward, so it has a maximum point (the vertex is the highest point). The value of \( b \) does not determine the presence of a maximum or minimum in this way. So the correct statement is about the sign of \( a \): if \( a \) is positive, it has a minimum; if \( a \) is negative, it has a maximum.

Answer:

If the 'a' is a positive, it has a minimum.
If the 'a' is a negative, it has a maximum.