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