Write an equation in vertex form for the parabola.

Question

The vertex is (5, 4) and it passes through (6, 1). It has to start with y=. Please help.

Answer 1

(5,4), (6,1) a parabola? An infinite number of equations starting y=

but take maybe the simplest. Let (6,1) be the vertex and minimum point of an upward opening parabola

then y=a(x-6)^2 + 1, to solve for a plug in the other point (5,4)

4 =a(5-6)^2+ 1 = a+1

a = 4-1 = 3

y =3(x-6)^2 +1 is in vertex form

But you could have a downward opening parabola with (5,4) as the vertex and maximum point

y=a(x-5)^2 + 4, plug in (6,1) to solve for a

1 =a +4

a =1-4 = -3

y=-3(x-5)^2 + 4