Express the function in vertex form given that it has the vertex (1,3) and passes through (-2,5). Does this function have a minimum or a maximum value?

Question

Express the function in vertex form given that it has the vertex (1,3) and passes through (-2,5). Does this function have a minimum or a maximum value?

Answer 1

y=a(x-h)²+k where the vertex = (h,k) and the graph contains the point P=(x,y)

So, v=(1,3) and P=(-2,5)

this means 5 = a(-2-1)²+3 —> 5 = 9a+3 —> a = 2/9

So: y = (2/9)(x-1)²+3

Since a>0, the graph has a minimum of y = 3