What happens when a quadratic function touches the x-axis only once? It means that the quadratic function has only one real zero. So which formula should we use? How about the almighty quadratic formula?
So when does the quadratic formula give you only one real zero? When the discriminant is equal to zero!
The discriminant is: b²-4ac
In our quadratic equation that means:
b = (3+m)
a = 4
c = 1
Thus, we need to solve: (3+m)²- 4*(4)*(1) = 0
m²+ 6m + 9 - 16 = 0
m² + 6m - 7 = 0
(m+7)(m-1) = 0
m = -7, 1
That's it! Plug back in and graph to see that it actually works!