State the coordinates of the vertex of the parabola ?

Question

State the coordinates of the vertex of the parabola whose equation is

y = 3(x - 2)2 + 5

(-2, -5)

(-2, 5)

(2, -5)

(2, 5)

none of these

I need to know how to do this please if anyone has a simple way of explaining this to me it would be great.

Answer 1

(2, 5)

One form of equation of a parabola is y = a(x ± b)^2 ± c where a, b & c can be any number, except a cannot be zero.

Vertex of a parabola would be (∓b, ±c). Look out for the sign in front of b.

ie.

y = a(x + b)^2 + c ===> (-b, c)

y = a(x - b)^2 + c ===> (b, c)

y = a(x + b)^2 - c ===> (-b, -c)

y = a(x - b)^2 - c ===> (b, -c)

In summary, vertex of a parabola if its equation is in this form is

y = a(x ± b)^2 ± c ===> (∓b, ±c)