SOLUTION: for what values of k will the function f(x)=x^2 +6x+k a) cut the a-axis twice b) touch the x-axis c) have no x- intercepts

Algebra ->  Quadratic-relations-and-conic-sections -> SOLUTION: for what values of k will the function f(x)=x^2 +6x+k a) cut the a-axis twice b) touch the x-axis c) have no x- intercepts       Log On


   

Question 422025: for what values of k will the function f(x)=x^2 +6x+k
a) cut the a-axis twice
b) touch the x-axis
c) have no x- intercepts
Answer by ewatrrr(24785) About Me  (Show Source):
You can put this solution on YOUR website!


Hi

Using the vertex form of a parabola, y=a%28x-h%29%5E2+%2Bk 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