X=3y^{2} -6y-4 :Graph

i know you make x zero but can not factor. What do i do now

X=3y^{2} -6y-4 :Graph

i know you make x zero but can not factor. What do i do now

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Recall that the x-intercept of a function is the point at which the graph of the function intersects the x-axis (i.e., the point at which y=0) and the y-intercept of a function is the point at which the graph of the function intersects the y-axis (i.e., the point at which x=0).

Thus, for the following function: x = 3y^{2} - 6y - 4

==> the x-intercept of the function is at the point (x, 0), and is determined by plugging in y=0

x = 3(0)^{2} - 6(0) - 4 = 0 - 0 - 4 = -4

x-intercept = (-4, 0)

==> the y-intercept of the function is at the point (0, y), and is determined by plugging in x=0

0 = 3y^{2} - 6y - 4

since this quadratic function cannot be factored, use the quadratic equation to solve for y...

....the quadratic equation is represented by the following formula:

x = (-b ± √(b^{2} - 4ac)) / 2a

the function in question is in terms of y, so x here is simply replaced with y

y = (-b ± √(b^{2} - 4ac)) / 2a , where a= 3 , b= -6 , c= -4

y = (-(-6) ± √((-6)^{2} - 4(3)(-4))) / 2(3)

= (6 ± √(36 - (-48))) / 6 = (6 ± √(36 + 48)) / 6

= (6 ± √(84)) / 6

= (6 ± √(4)·√(21)) / 6

= (6 ± 2√(21)) / 6

= (6/6) ± (2√(21)/6)

= 1 ± √(21)/3

therefore, the y-intercept is at two points on the graph of the function:

(0, (1 + √(21)/3)) and (0, (1 - √(21)/3))

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