Answer:
1/36
Step-by-step explanation:
When the coefficient is 1, the function has zeros at -3 and -5, one horizontal unit from the vertex. You want to move the zero to (2, 0), which is 6 units from the vertex. To achieve a horizontal stretch by a factor of 6, the value of x in the function must be replaced by x/6. That would make the coefficient of x^2 be (1/6)^2 = 1/36.
The coefficient of the squared term is 1/36.
Check the picture below. So the parabola looks more or less like so.
let's recall that the vertex is half-way between the focus point and the directrix, at "p" units away from both.
Let's notice that the focus point is below the directrix, that means the parabola is vertical, namely the squared variable is the "x", and it also means that it's opening downwards as you see in the picture, namely that "p" is negative, in this case "p" is 1 unit, and thus is -1.
