Answered

Which equation has exactly one solution?

A4\(x^{2}\) - 12x - 9 = 0
B4\(x^{2}\) + 12x + 9 = 0
C4\(x^{2}\) - 6x - 9 = 0
C4\(x^{2}\) + 6x + 9 = 0

(Please show how you get the answer)

Verified Answer :

I would answer this by using the quadratic formula to figure out which equation only has one solution.
quadratic formula: (-b(+or-)√(b^2-(4ac)))/2a.
You find that the equation 4x²+12x+9=0 only has the root of x=-1.5.

Since the solution is where the parabola crosses the x-axis, you can also figure out which equation has only one solution by whether or not the axis of symmetry lands is a solution or not.  If the axis of symmetry is a solution, the function only has one solution (that being the vertex).  If the axis of symmetry is not a solution, the function has to have either two or no roots.  You can find the axis of symmetry by using the equation x=-b/2a.  Using that equation you can find that the equation 4x²+12x+9 has the axis of symmetry being at x=-1.5 which means that the vertex is (-1.5,0).  Since the equation 4x²+12x+9 has its vertex at (-1.5,0) and the vertex is the lowest or highest point of the function, that function only has one x-intercept meaning it only has 1 solution.  

I hope this helps.  Let me know in the comments if anything is unclear.

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