SOLUTION: f(x) = c (x - 3)(x + 3) In the quadratic equation above, c is a nonzero constant. The graph of the equation in the xy- plane is a parabola with a vertex (h,k), where k = -18. Wh

Algebra ->  Quadratic-relations-and-conic-sections -> SOLUTION: f(x) = c (x - 3)(x + 3) In the quadratic equation above, c is a nonzero constant. The graph of the equation in the xy- plane is a parabola with a vertex (h,k), where k = -18. Wh      Log On


   

Question 1183440: f(x) = c (x - 3)(x + 3)
In the quadratic equation above, c is a nonzero constant. The graph of the equation in the xy- plane is a parabola with a vertex (h,k), where k = -18. What is c?
Found 2 solutions by Boreal, ikleyn:
Answer by Boreal(15235) About Me  (Show Source):
You can put this solution on YOUR website!
k is the constant and is -18
the product of the parentheses is -9
c must be 18/-9 or -2
the equation is f(x)=2x^2-18
graph%28300%2C300%2C-10%2C10%2C-20%2C20%2C2%28x-3%29%28x%2B3%29%29

Answer by ikleyn(52796) About Me  (Show Source):
You can put this solution on YOUR website!
.

The x-coordinate of the vertex is exactly half way between the roots  h = %28%28-3%29+%2B+3%29%2F2 = 0%2F2 = 0.


Hence, the vertex is located at  (0,-18).


It means that the value of the quadratic polynomial at x = 0 is -18.


So, we substitute x= 0 into the polynomial and equate it to -18


    c*(0-3)*(0+3 = c*(-9) = -18,

or

    -9c = -18.


It gives the value of "c"   c = %28-18%29%2F%28-9%29 = 2.      ANSWER


                See the plot below


    graph%28300%2C300%2C-10%2C10%2C-20%2C20%2C2%28x-3%29%28x%2B3%29%29



              Plot y = 2(x-3)*(x+3).

Solved.