Which statements are true about all points on the x-axis? check all that apply.
they have a y-value of 0.
they have an x-value that is not 0.
they are not to the left or to the right of the origin.
they are in quadrant i.
they are not in any of the quadrants.
they are not above or below the origin.
answer the question correctly.

The statements "they have a y-value of 0", "they are not in any of the quadrants", and "they are not above or below the origin" are correct.

Let a point on the x-axis. The following observations can be made about the point:

From the above points, it can be concluded that statements 1, 5, and 6 are correct.

Therefore, the statements "they have a y-value of 0", "they are not in any of the quadrants", and "they are not above or below the origin" are correct.

For more details, refer to the link:

link

For any point on the x-axis...

They have a y-value of 0 (The equation of the x axis is "y=0"!)

They have a x-value that is not 0. (No, point (0,0) has x value of 0)

They are not to the left or to the right of the origin. (All points except one are so no.)

They are in Quadrant I. (No, they do not lie in any quadrant.)

They are not in any of the quadrants. (Yes.)

They are not above or below the origin. (Yes.)

statment 1, 5, and 6

step-by-step explanation:

equation

you are asked to write the equation

  expression = 0

using the given expression. when you do that, you have

  2x^2-2x-12 = 0

factoring

you can see that each of the coefficients is even, so a factor of 2 can be removed immediately.

  2(x^2 -x -6) = 0

if you multiply the binomials (x+a)(x+b), you get

  (x +a)(x +b) = x^2 +(a+b)x +ab

this tells you the coefficient of x is the sum of two factors of the constant term. here, that means -1 is the sum of two factors of -6. we want to know those factors so we can factor the trinomial.

  -6 = -1×6 = -2×3 = -3×2 = -6×1

the factor pair that sums to -1 is {-3, 2}, so our factorization is

  2(x -3)(x +2) = 0

solutions

the solutions to this equation are the values of x that make the product zero. a product is zero only when only of the factors of the product is zero. here, that means

  x - 3 = 0

  x = 3 . . . add 3 to both sides of the equation

or

  x +2 = 0

  x = -2 . . . add -2 to both sides of the equation

the solutions to the equation are x=3 or x=-2. both of these values of x satisfy the equation—they make it be true.

answer:

c. the third graph