Question

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

Answer 1

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.