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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.

Respuesta :

\left[y \right] = \left[ 2\,x2\right][y]=[2x2]

Answer:

D) The graphs are symmetric about the y-axis.

Step-by-step explanation:

The given equations are

[tex]y=-\frac{1}{2}x^{2} +2\\y=-\frac{3}{4} x^{2} \\y=-\frac{4}{5}x^{2} -5\\y=-2x^{2} +3[/tex]

Notice that all given equations have a negative quadratic term.

Remember that the form of a quadratic equation is

[tex]y=ax^{2} +bx+c[/tex]

Where [tex]a[/tex] is the coefficient of the quadratic term.

When [tex]a<0[/tex], 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.

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