Question

The vertex of the parabola below is at the point (1,3), and the point (2,6) is

on the parabola. What is the equation of the parabola?

O A. y=3(x+ 1)2-3

O B. y=3(x-1)2 + 3

O c. x= 2(y - 3)2 + 1

O D. y=6(x-1)2 + 3

Answer 1

B. y=3(x-1)2 + 3

Explanation:

Given that

vertex of the parabola is at the point (1,3)

let's verify, if the option B is the correct equation of the parabola.

`y=3(x-1)^2 + 3\\ \\y=3(x^2+1-2x) + 3\\\\y=3x^2+3-6x + 3\\\\y=3x^2-6x + 6....Eq1`

comparing to standard equationof parabola (standard quadratic equation), we get

`a=3, b=-6 and c=6`

to find the vertex we use formula for x- coordinate as
`x=-b/2a`

`x=-(-6)/2(3)\\\\x=6/6\\x=1`

to find y put x=1 in the Eq1, we get

`y=3(1)^2-6(1)+6\\\\y=3-6+6\\\\y=3`

vertex =(x,y) = (1, 3)

thus vertex of the parabola from the equation y=3(x-1)2 + 3 is (1,3), thus verified