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

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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)   (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
Answer by ikleyn(52798)   (Show Source): You can put this solution on YOUR website!
.

The x-coordinate of the vertex is exactly half way between the roots  h =  =  = 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 =  = 2.      ANSWER


                See the plot below


    



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

Solved.



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