SOLUTION: Please help me find the y -intercept and x intercepts of this function: {{{f(x)= sqrt(8x^2 +4x)}}}

Algebra ->  Rational-functions -> SOLUTION: Please help me find the y -intercept and x intercepts of this function: {{{f(x)= sqrt(8x^2 +4x)}}}       Log On


   

Question 789278: Please help me find the y -intercept and x intercepts of this function: f%28x%29=+sqrt%288x%5E2+%2B4x%29
Answer by fcabanski(1391) About Me  (Show Source):
You can put this solution on YOUR website!
f(x) in function notation is the same as y. f(x)=x is the same as y=x.


x intercept is when y=0 (when the function touches the x axis). y intercept is when x=0 (when the function touches the y axis.) Find the x intercept by setting y = 0 then solving the equation for x. Find the y intercept by setting x=0 then solving the equation for y.


y intercept: y=+sqrt%288x%5E2+%2B+4x%29. Set x=0: y=+sqrt%288%2A0%5E2+%2B+4%2A0%29+=+sqrt%280%29+=+0 The y intercept is y=0.


x intercept: y=+sqrt%288x%5E2+%2B+4x%29 set y=0: 0=+sqrt%288x%5E2+%2B+4x%29 square both sides 0=+8x%5E2+%2B+4x


4x(2x+1) = 0


Either factor can = 0.


4x=0


x=0 is one x intercept.


(2x+1)=0


2x = -1


x = -1/2 is the other x intercept.