SOLUTION: Hello, I need help with this question, it says: Find the discriminant of sqrt((-12)^2 - 4 * 9 * 3), identify the number of the solutions and their types. Graph the possible quad

Question 999340: Hello,
I need help with this question, it says: Find the discriminant of sqrt((-12)^2 - 4 * 9 * 3), identify the number of the solutions and their types. Graph the possible quadratic function.
I ended up with +6 and -6 but I have no idea where to go from there or how to graph it. Do I plug in -b and complete the quadratic function or what??
Help me please!
Found 2 solutions by MathLover1, rothauserc:
Answer by MathLover1(20849) (Show Source): You can put this solution on YOUR website!

the discriminant of
so, the discriminant is and ; that means quadratic function has solutions
now, we can find what is the equation:
recall: the discriminant is
when you compare it to given above, , you see that , , and
so, the possible quadratic function is and it has solutions
let's find them:
make
...both sides divide by
....factor
...group

solutions:
if =>=>
=>
see it on the graph:

Answer by rothauserc(4718) (Show Source): You can put this solution on YOUR website!
the quadratic formula for solutions of x is
x = (-b + sqrt(b^2 - 4ac)) / 2a
x = (-b - sqrt(b^2 - 4ac)) / 2a
you are given the sqrt in order to calculate the discriminant
sqrt((-12)^2 - 4 * 9 * 3) = sqrt(144 - 108) = 6
x = (-(-12) + 6) / (2 * 9) = 18 / 18 = 1
x = (-(-12) -6) / (2 * 9) = 6 / 18 = 1/3
there are two solutions 1, 1/3 both are rational numbers which are real numbers
**************************************************************************
f(x) = 9x^2 -12x +3
**************************************************************************
here is the function's graph

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