Answer:
[tex]\boxed{\bold{y=\frac94\left(x+\frac23\right)^\big{\bold2}-\,2}}[/tex]
Step-by-step explanation:
[tex]y=\frac94x^2+3x-1\\\\y=\frac94(x^2+\frac49\cdot3x-\frac49)\\\\y=\frac94\big(\underline{x^2+2\cdot x\cdot\frac23+(\frac23)^2}-(\frac23)^2-\frac49\big)\\\\y=\frac94\big((x+\frac23)^2-\frac49-\frac49\big)\\\\y=\frac94(x+\frac23)^2-1-1\\\\\underline{y=\frac94(x+\frac23)^2-2}[/tex]
