Question

Find the vertex of this parabola. y=-2x+4x+12

Answer 1

(1,14)

Explanation:

Answer 2

Vertex of the parabola is ( 1 , 14 ).

Explanation:

Given Equation of parabola is
`y=-2^2+4x+12`

We have to find the vertex of the parabola.

We first convert the given equation of parabola in standard equation of parabola using completing the square method.

Standard equation of parabola,

`(x-h)^2=4a(y-k)`

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

consider,

y = -2x² + 4x + 12

y = -2( x² - 2x - 6 )

y = -2 ( x² - 2x + 1² - 1² - 6 )

y = -2 ( x -1 )² - 7 × ( -2 )

y - 14 = -2 ( x - 1 )²

`(x-1)^2=(1)/(2)(y-14)`

By comparing,

vertex = ( 1 , 14 )

Therefore, Vertex of the parabola is ( 1 , 14 ).