Y= - 1 2 x2 + 2 y = - 3 4 x2 y = - 4 5 x2 - 5 y = -2x2 + 3 for the quadratic equations shown here, which statement is true? a) the graphs open upward. b) the graphs are symmetric about the line x = 1. c) the graphs are listed from narrowest to widest. d) the graphs are symmetric about the y-axis.

Step-by-step explanation:

The given equations are

Notice that all given equations have a negative quadratic term.

Remember that the form of a quadratic equation is

Where is the coefficient of the quadratic term.

When , the parabola that represents the equation opens downward, because the quadratic term is negative.

Therefore, in this case, the common charactersitc between all equations is that they all represent a parabola which opens downward.

However, there's another characteristic. All parabolas are symmetrical about the y-axis, because the square power has only x-variable inside.

Therefore, the right answer is D.