The Quadratic Formula is -b +/- sqrt(b^2 - 4ac) all divided by 2a.
What's inside the square root is the discriminant. if it = 0, there is one solution repeated twice.
ax^2-6x+3 - that has to be ax^2 -6x + c. Otherwise c=3
(-6)^2 - 4ac = 0
36 - 4ac = 0
4ac = 36
ac = 9
So a can be 3 and c 3, or a=1 and c=9 or a=9 and c=1.
y = 3x^2 - 6x + 3 is one answer. Another is y = x^2 - 6x + 9, and another is y = 9x^2 - 6x + 1.
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ax^2 + 6x + c = 0 To have two real solutions, the discriminant has to be positive (greater than 0)
6^2 - 4ac > 0
36 - 4ac > 0
36 > 4ac
9 > ac
a=1 c=1 is one possibility.
y = x^2 + 6x + 1
