Question

Y=4x^2+7x vertex form

Answer 1

Use completing the square:

Ex:

`y = x^2 +4x \\ \\ y= x^2 +4x +((4)/(2))^2- ((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 + (7)/(4)x)`
Apply completing the square:

`y = 4(x^2 + (7)/(4)x +((7/4)/(2))^2 -((7/4)/(2))^2) \\ \\ y = 4[(x^2 + (7)/(4)x+(49)/(64)) - (49)/(64) ] \\ \\ y = 4(x + (7)/(8))^2 - (49)/(16)`