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 $=(-3\frac{1}{2},-13\frac{1}{2})$

Step-by-step explanation:

Given equation of parabola is

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

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

$\Leftrightarrow y =2(x^2 + 2\times \frac{ 7}{2}x+\frac{49}{4}-\frac{49}{4}+\frac {11}{2})$

$\Leftrightarrow y =2[(x + \frac{ 7}{2})^2-\frac{27}{4})]$

$\Leftrightarrow y =2(x + \frac{ 7}{2})^2-\frac{27}{2}$

$\Leftrightarrow y+\frac{27}{2} =2(x + \frac{ 7}{2})^2$

Therefore the vertex of the parabola is  $(-\frac{7}{2},-\frac{27}{2})$ $=(-3\frac{1}{2},-13\frac{1}{2})$