Question

Y=4x^2+7x vertex form

Answer 1

Use completing the square:

Ex:
$y = x^2 +4x \\ \\ y= x^2 +4x +(\frac{4}{2})^2- (\frac{4}{2})^2 \\ \\ y = (x^2 +4x+4) - 4 \\ \\ y = (x+2)^2 - 4$

Now apply to your problem.
First factor out the '4' in front of the 'x^2' term
$y = 4(x^2 + \frac{7}{4}x)$
Apply completing the square:
$y = 4(x^2 + \frac{7}{4}x +(\frac{7/4}{2})^2 -(\frac{7/4}{2})^2) \\ \\ y = 4[(x^2 + \frac{7}{4}x+\frac{49}{64}) - \frac{49}{64} ] \\ \\ y = 4(x + \frac{7}{8})^2 - \frac{49}{16}$