You need to write the quadratic equation that is congruent to the function `y = 3x^2` , it opens down and it has a vertex at `(1,5)` .
You should know that two functions are congruent if they have the same attributes.
Hence, comparing the general form of quadratic function `y = ax^2 + bx + c` to the congruent function `y = -3x^2` , yields that a = -3. Since the problem provides the information that parabola opens down, hence a needs to be negative.
You also know that if the vertex `V(h,k)` of the parabola is given, you may write the vertex form of quadratic such that:
`y = a(x-h)^2 + k`
Hence, given the vertex `(1,5)` and the coefficient `a = -3` , you may write the vertex form of parabola such that:
`y = -3(x - 1)^2 + 5`
Hence, evaluating the vertex form of parabola, under the given condition, yields `y = -3(x - 1)^2 + 5` , hence, the first option matches the best.