How do you write the equation of this description: the graph of a parabola has a vertex of (2,3) and vertically stretched by 3

The equation of parabola is y = 3x² - 12x + 15.

Step-by-step explanation:

The equation of the parabola is given as y = x².

If it has a vertex then the equation can be written as,

y = a (x-h) ² + k

where (h, k) is the vertex and a is the stretching or compressing factor.

So here the vertex is (2,3) and it is vertically stretched by 3.

So the equation is given as,

y = 3 (x-2) ² + 3

y = 3 (x² - 4x+4) + 3

= 3x² - 12x + 12 + 3

y = 3x² - 12x + 15 is the equation of the parabola.