write equation of parabola that has vertex (2,0) and goes through point (1,3)

Question

write equation of parabola that has vertex (2,0) and goes through point (1,3)

 

 

show work please

Answer 1

The equation for a parabola is y = k(x-a)² + b, where (a, b) is the vertex.

 

Since the vertex is at (2,0), this means that the equation is y = k (x - 2)² + 0 = k (x - 2)²

 

Since it goes through (1,3), plug x=1 and y=3 into that equation to find k:

y = k (x - 2)²

3 = k (1 - 2)²

3 = k (-1)²

3 = k

 

So the equation is y = 3(x - 2)²