If a quadratic equation has a discriminant that equals zero, which of the following statements is always true?

a. the equation has two solutions and the parabola will open upward.
b. the equation has one solution and the parabola will open downward.
c. the equation has zero solutions and there is not enough information to determine the direction of the parabola.
d. the equation has one solution and there is not enough information to determine the direction of the parabola.

d. The equation has one solution and there is not enough information to determine the direction of the parabola.

Step-by-step explanation:

For a general quadratic equation

y = ax² +bx +c

the solution is

The discriminant (D) is the part of the quadratic formula underneath the radical: b² - 4ac.

D tells us whether there are

If D= 0,

and there are two identical solutions ("one solution").

The direction of the parabola depends on the sign of a.

That information is not given, so we cannot determine the direction of the parabola.

d, x=8

step-by-step explanation:

simplifying

4x + -5 = 2x + 11

reorder the terms:

-5 + 4x = 2x + 11

reorder the terms:

-5 + 4x = 11 + 2x

solving

-5 + 4x = 11 + 2x

solving for variable 'x'.

move all terms containing x to the left, all other terms to the right.

add '-2x' to each side of the equation.

-5 + 4x + -2x = 11 + 2x + -2x

combine like terms: 4x + -2x = 2x

-5 + 2x = 11 + 2x + -2x

combine like terms: 2x + -2x = 0

-5 + 2x = 11 + 0

-5 + 2x = 11

add '5' to each side of the equation.

-5 + 5 + 2x = 11 + 5

combine like terms: -5 + 5 = 0

0 + 2x = 11 + 5

2x = 11 + 5

combine like terms: 11 + 5 = 16

2x = 16

divide each side by '2'.