Hi

Using the vertex form of a parabola,  where(h,k) is the vertex

for what values of k will the function f(x)=x^2 +6x+k

f(x)=x^2 +6x+k = (x+3)^2 -9 +k     |completing the square

Note parabola opens upward(coefficient of the squared term >0)

a) cut the a-axis twice (-9+k)<0     or k < 9  Vertex below the x-axis

b) touch the x-axis (-9+k) = 0       or k = 9

c) have no x- intercepts (-9+k)> 0   or k > 9  Vertex above the x-axis

 



 

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