Question

ASAP PLEASE

The equation of a parabola is y = 2x^2 + 14x + 11
Write the equation in vertex form.
Simplify any fractions.

Answer 1

Therefore the vertex of the parabola is
`=(-3(1)/(2),-13(1)/(2))`

Explanation:

Given equation of parabola is

`y =2 x^2 + 14x +11`

`\Leftrightarrow y =2(x^2 + 7x+\frac {11}{2})`

`\Leftrightarrow y =2(x^2 + 2* ( 7)/(2)x+(49)/(4)-(49)/(4)+\frac {11}{2})`

`\Leftrightarrow y =2[(x + ( 7)/(2))^2-(27)/(4))]`

`\Leftrightarrow y =2(x + ( 7)/(2))^2-(27)/(2)`

`\Leftrightarrow y+(27)/(2) =2(x + ( 7)/(2))^2`

Therefore the vertex of the parabola is
`(-(7)/(2),-(27)/(2))`
`=(-3(1)/(2),-13(1)/(2))`