Answer:
-2/3(x-3/2) + 9/2 = y
Step-by-step explanation:
SO this is the symmetric form of the quadratic function where it is presented as a(x-x1)(x-x2), where x1 and x2 are x values when y = 0. The standard form is represented as a(x-h)^2 + k, where a is the same for both forms, but (h,k) is the coordinate for the vertex, or highest/lowest point of the function.
To find h you have to check the distance between x1 and x2 and divide by 2. So 3 and 6 would be 3, and h is 3/2. (remember that if symmetric form is something like a(x+3)(x+6), x1 and x2 are -3 and -6 because thats how it is.)
To find k, you plug in h to the equation.
-2/3(3/2 - 3)(3/2 - 6) = y
-2/3(-3/2)(-9/2) = y
y = -9/2
so h and k are 3/2 and -9/2
So the standard form would be -2/3(x-3/2) - 9/2
Hope that answers your question
