Question

The vertex of the parabola is at the point (2,-5). which of the equations below could be the one for this parabola?

Answer 1

Hello,
Answer is Dsince y=k(x-2)²-5 and if k=1 ==>D.

Answer 2

The correct option is D.
`y=(x-2)^(2)-5`

Explanation:

If the vertex V of the parabola has the following coordinates :

`V=(xV,yV)`

One way to write the equation of the parabola is :

`y=a(x-xV)^(2)+yV`

Where xV and yV are the coordinates from the vertex of the parabola and ''a'' is a real number.

If
`a>0` ⇒ The parabola is concave upward

If
`a<0` ⇒ The parabola is concave downward

In this exercise

`V=(xV,yV)=(2,-5)` ⇒

One way to write this parabola is

`y=a(x-2)^(2)-5`

The graph of the parabola is concave upward ⇒
`a>0`

The option D. is

`y=1(x-2)^(2)-5` Where
`a=1` and
`1>0` ⇒

The correct option is D.