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

Algebra ->  Graphs -> 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      Log On


   

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) About Me  (Show Source):
You can put this solution on YOUR website!

the discriminant of sqrt%28%28-12%29%5E2+-+4+%2A+9+%2A+3%29=sqrt%28144+-+108%29=sqrt%2836%29
so, the discriminant is 36 and 36%3E0; that means quadratic function has two real solutions
now, we can find what is the equation:
recall: the discriminant is b%5E2+-+4+%2A+a%2A+c
when you compare it to given above, %28-12%29%5E2+-+4+%2A+9+%2A+3%29, you see that b=+-12, a=9, and c=3
so, the possible quadratic function is y=9x%5E2-12x%2B3 and it has two real solutions
let's find them:
make y=0
0=9x%5E2-12x%2B3...both sides divide by 3
0=3x%5E2-4x%2B1....factor
0=3x%5E2-3x-x%2B1...group
0=%283x%5E2-3x%29-%28x-1%29
0=3x%28x-1%29-%28x-1%29
0=%283x-1%29%28x-1%29
solutions:
if 0=%283x-1%29=>3x=1=>highlight%28x=1%2F3%29
0=%28x-1%29=>highlight%28x=1%29
see it on the graph:
+graph%28+600%2C+600%2C+-5%2C+5%2C+-10%2C+10%2C+9x%5E2-12x%2B3%29+






Answer by rothauserc(4718) About Me  (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
+graph%28+300%2C+200%2C+-6%2C+5%2C+-10%2C+10%2C+9x%5E2+-12x+%2B3%29+