Question

The vertex if the parabola below is at the point (2,4) and the point (3,6) is on the parabola. What is the equations the parabola

Answer 1

I think the equation is 2(x-2)^2+4

Answer 2

`y = 2(x-2)^2+4` is the equations the parabola

Explanation:

The standard equation of parabola is given by:

`y = a(x-h)^2+k` ....[1]

where,

a is the non zero real number and

(h, k) is the vertex of the parabola.

As per the statement:

The vertex if the parabola below is at the point (2,4)

⇒
`(h, k) = (2, 4)`

⇒h =2 and k =4

Substitute these in [1] we have;

`y = a(x-2)^2+4`

Since, the point (3,6) is on the parabola

⇒x = 3 and y = 6

then;

`6 = a(3-2)^2+4`

`6 = a+4`

Subtract 4 from both sides we have:

2= a

or

a = 2

⇒
`y = 2(x-2)^2+4`

Therefore, the equations the parabola is,
`y = 2(x-2)^2+4`