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How to find x and y intercept

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2 Answers

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 = 3y2 - 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 = 3y2 - 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 ± √(b2 - 4ac)) / 2a

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

                y = (-b ± √(b2 - 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))

You are correct about how to find the y-intercepts: you make x zero and solve for y. Unfortunately you won't be able to factor the right side of the equation, so you will have to use the quadratic equation. In this case, since you're solving for y (most times you're solving for x), y = [-b +/- sqrt(b^2-4ac)]/2a, or y equals negative b plus or minus the square-root of b squared minus 4 times a times c, all over 2 times a, where a, b and c are the coefficients 3, -6 and -4 respectively. You should get 1 plus or minus one-third times the square-root of 21 To get the x intercept, simply plug in zero for y.