SOLUTION: For what value(s)of k will the graph of y=3x^2+(k+2)x+3 touch the x-axis at exactly one point

Algebra.Com
Question 184671: For what value(s)of k will the graph of y=3x^2+(k+2)x+3 touch the x-axis at exactly one point
Answer by josmiceli(19441)   (Show Source): You can put this solution on YOUR website!

Instead of 2 roots, and ,
There will be a double root,


-------------------------


I can make the substitutions



and

-------------------------



and



The graph touches the x-axis when or
for :



for :


I'll plot both:


RELATED QUESTIONS

for what value(s) of k will the graph of y = x^2-3x+k a) touch the x-axis b) never (answered by jim_thompson5910)
Find the value/s of k for which the circle x^2+y^2=4 and (x-4)^2 + (y-3)^2=k^2 intersect... (answered by josgarithmetic,ikleyn,MathTherapy)
Determine the value of k such that g(x)= 3x + k intersects the quadratic function... (answered by Fombitz,richard1234)
For what value of k does the following system have exactly one solution? y=x^2... (answered by greenestamps)
hey, could you please solve the following question, thanks, The graph of function y=... (answered by stanbon,ankor@dixie-net.com)
for what values of k will the function f(x)=x^2 +6x+k a) cut the a-axis twice b)... (answered by ewatrrr)
For what value/s of k will the system of equations x^2 + y^2 = 4 and y=kx+4 have exactly (answered by ikleyn)
For what positive value of k is the graph of y = kx^2 + 6x + k +8 tangent to the x... (answered by drk)
Consider the graph y=(x-k)^2 where k is any interger. What effect does changing the value (answered by Edwin McCravy)