# The parabola #f(x) = x^2 + 2(m+1)x + m + 3# is tangent to #x# axis in the negative side. What is the value of #m# ?

##### 1 Answer

#### Explanation:

#f(x) = x^2+2(m+1)x+m+3#

#=(x+(m+1))^2-(m+1)^2+m+3#

#=(x+(m+1))^2-m^2-m+2#

This is in vertex form with intercept

In order for it to be tangential to the

#0 = -m^2-m+2 = (2+m)(1-m)#

So

If

If

**Alternative method**

This is of the form

It has discriminant

#Delta = b^2-4ac = (2(m+1))^2-4(1)(m+3)#

#=4(m^2+2m+1-m-3)#

#=4(m^2+m-2) = 4(m+2)(m-1)#

If the parabola is tangential to the

Hence

If

If