Find The Equation. the vertex is (4,1) and contains the point (2,3)

Question

this is a writing quadratic function problem.HELP

Answer 1

I don't know if there is a method you are supposed to use, but the formula is easy to deduce.

 

axis of symmetry is x = 4  and the f(4) =1, so

 

y = a(x - 4)² + 1

 

If a  were 1 the a difference of 2 along the x-axis would yield a change of 4 along the y-axis, but it is half that, so a = 1/2

 

y= (1/2)(x - 4)² + 1

 

check by substitution

 

y = (1/2)[(2) - 4]² + 1

y = (1/2) (-2)² + 1

y = (1/2)(4) + 1

y = 2 + 1 = 3