Question

The equation of a parabola is given.

y=−14x2+4x−19



What are the coordinates of the vertex of the parabola?



Enter your answer in the boxes.

Answer 1

The coordinates are 8, -3.

Answer 2

vertex (
`(1)/(7)`,
`(131)/(7)`).

Explanation:

Given : The equation of a parabola is given.

y=−14x²+4x−19

To find : What are the coordinates of the vertex of the parabola.

Solution : We have given that

y = −14x²+4x−19

we will be "completing the square" .

Factor out -14 to make leading coefficient 1

y = -14 (
`x^(2) -(2x)/(7) +(19)/(14)`)

Add and subtract
`((-1)/(7)) ^(2)`

y = -14 (
`x^(2) -(2x)/(7) +(19)/(14)+(-1)/(7)) ^(2) - ((-1)/(7))^(2))` .

Complete the square

y = -14 (
`(x -(1)/(7)) ^(2) +(19)/(14)- ((-1)/(7))^(2))`.

y = -14 (
`(x-(1)/(7)) ^(2) -(131)/(7)`

Standard form of parabola vertex form y = a(x - h)²+ k,

Where, ( h, k) are vertex

On comparing a = -14 , h=
`(1)/(7)`, k =
`(131)/(7)`

Therefore, vertex (
`(1)/(7)`,
`(131)/(7)`).